Pub Date : 2026-01-01DOI: 10.1016/j.jpaa.2025.108145
Shamik Das, Somnath Jha
We consider certain families of integers n determined by some congruence condition, such that the global root number of the elliptic curve is 1 for every n, however a given n may or may not be a sum of two rational cubes. We give explicit criteria in terms of the 2-parts and 3-parts of the ideal class groups of certain cubic number fields to determine whether such an n is a cube sum. In particular, we study integers n divisible by 3 such that the global root number of is 1. For example, for a prime , we show that for 3ℓ to be a sum of two rational cubes, it is necessary that the ideal class group of contains as a subgroup. Moreover, for a positive proportion of primes , 3ℓ can not be a sum of two rational cubes. A key ingredient in the proof is to explore the relation between the 2-Selmer group and the 3-isogeny Selmer group of with the ideal class groups of appropriate cubic number fields.
{"title":"On certain root number 1 cases of the cube sum problem","authors":"Shamik Das, Somnath Jha","doi":"10.1016/j.jpaa.2025.108145","DOIUrl":"10.1016/j.jpaa.2025.108145","url":null,"abstract":"<div><div>We consider certain families of integers <em>n</em> determined by some congruence condition, such that the global root number of the elliptic curve <span><math><msub><mrow><mi>E</mi></mrow><mrow><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub><mo>:</mo><msup><mrow><mi>Y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi>X</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is 1 for every <em>n</em>, however a given <em>n</em> may or may not be a sum of two rational cubes. We give explicit criteria in terms of the 2-parts and 3-parts of the ideal class groups of certain cubic number fields to determine whether such an <em>n</em> is a cube sum. In particular, we study integers <em>n</em> divisible by 3 such that the global root number of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span> is 1. For example, for a prime <span><math><mi>ℓ</mi><mo>≡</mo><mn>7</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>9</mn><mo>)</mo></math></span>, we show that for 3<em>ℓ</em> to be a sum of two rational cubes, it is necessary that the ideal class group of <span><math><mi>Q</mi><mo>(</mo><mroot><mrow><mn>12</mn><mi>ℓ</mi></mrow><mrow><mn>3</mn></mrow></mroot><mo>)</mo></math></span> contains <span><math><mfrac><mrow><mi>Z</mi></mrow><mrow><mn>6</mn><mi>Z</mi></mrow></mfrac><mo>⊕</mo><mfrac><mrow><mi>Z</mi></mrow><mrow><mn>3</mn><mi>Z</mi></mrow></mfrac></math></span> as a subgroup. Moreover, for a positive proportion of primes <span><math><mi>ℓ</mi><mo>≡</mo><mn>7</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>9</mn><mo>)</mo></math></span>, 3<em>ℓ</em> can not be a sum of two rational cubes. A key ingredient in the proof is to explore the relation between the 2-Selmer group and the 3-isogeny Selmer group of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span> with the ideal class groups of appropriate cubic number fields.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108145"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-01DOI: 10.1016/j.jpaa.2025.108166
Nikita A. Karpenko
Given a reductive algebraic group G, we introduce a notion of consistent projective G-homogeneous variety X. For instance, the variety of Borel subgroups in G is consistent; if G is of inner type, all projective G-homogeneous varieties are consistent.
Our main result describes the summands in the complete motivic decomposition of X. It extends an earlier result of the author providing the same for G of inner type.
{"title":"Consistent varieties and their complete motivic decompositions","authors":"Nikita A. Karpenko","doi":"10.1016/j.jpaa.2025.108166","DOIUrl":"10.1016/j.jpaa.2025.108166","url":null,"abstract":"<div><div>Given a reductive algebraic group <em>G</em>, we introduce a notion of <em>consistent</em> projective <em>G</em>-homogeneous variety <em>X</em>. For instance, the variety of Borel subgroups in <em>G</em> is consistent; if <em>G</em> is of inner type, all projective <em>G</em>-homogeneous varieties are consistent.</div><div>Our main result describes the summands in the complete motivic decomposition of <em>X</em>. It extends an earlier result of the author providing the same for <em>G</em> of inner type.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108166"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-15DOI: 10.1016/j.jpaa.2025.108165
Clémence Chanavat, Amar Hadzihasanovic
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict ω- categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the expected properties: they include all degenerate cells, are closed under 2-out-of-3, and satisfy an appropriate version of the “division lemma”, which ensures that enwrapping a diagram with equivalences at all sides is an invertible operation up to higher equivalence. On the way to this result, we develop methods, such as an algebraic calculus of natural equivalences, for handling the weak units and unitors which set this framework apart from strict ω- categories.
{"title":"Equivalences in diagrammatic sets","authors":"Clémence Chanavat, Amar Hadzihasanovic","doi":"10.1016/j.jpaa.2025.108165","DOIUrl":"10.1016/j.jpaa.2025.108165","url":null,"abstract":"<div><div>We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict <em>ω</em>-<!--> <!-->categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the expected properties: they include all degenerate cells, are closed under 2-out-of-3, and satisfy an appropriate version of the “division lemma”, which ensures that enwrapping a diagram with equivalences at all sides is an invertible operation up to higher equivalence. On the way to this result, we develop methods, such as an algebraic calculus of natural equivalences, for handling the weak units and unitors which set this framework apart from strict <em>ω</em>-<!--> <!-->categories.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108165"},"PeriodicalIF":0.8,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108148
Marian Aprodu , Andrea Bruno , Edoardo Sernesi
The present paper is a natural continuation of the previous work [2] where we studied the second syzygy scheme of canonical curves. We find sufficient conditions ensuring that the second syzygy scheme of a genus–g curve of degree at least coincides with the curve. If the property is satisfied, the equality is ensured by a more general fact emphasized in [2]. If fails, then the analysis uses the known case of canonical curves.
{"title":"The second syzygy schemes of curves of large degree","authors":"Marian Aprodu , Andrea Bruno , Edoardo Sernesi","doi":"10.1016/j.jpaa.2025.108148","DOIUrl":"10.1016/j.jpaa.2025.108148","url":null,"abstract":"<div><div>The present paper is a natural continuation of the previous work <span><span>[2]</span></span> where we studied the second syzygy scheme of canonical curves. We find sufficient conditions ensuring that the second syzygy scheme of a genus–<em>g</em> curve of degree at least <span><math><mn>2</mn><mi>g</mi><mo>+</mo><mn>2</mn></math></span> coincides with the curve. If the property <span><math><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> is satisfied, the equality is ensured by a more general fact emphasized in <span><span>[2]</span></span>. If <span><math><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> fails, then the analysis uses the known case of canonical curves.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108148"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108157
Jiayi Chen , Bangming Deng , Shiquan Ruan
This paper deals with the triangle singularity defined by the equation for a weight triple , as well as the category of coherent sheaves over the weighted projective line defined by f. We calculate Hall polynomials associated with extension bundles, line bundles and torsion sheaves over . By using derived equivalence, this provides a unified conceptual method for calculating Hall polynomials for representations of tame quivers obtained by Szántó and Szöllősi (2024) [35].
{"title":"Hall polynomials for weighted projective lines","authors":"Jiayi Chen , Bangming Deng , Shiquan Ruan","doi":"10.1016/j.jpaa.2025.108157","DOIUrl":"10.1016/j.jpaa.2025.108157","url":null,"abstract":"<div><div>This paper deals with the triangle singularity defined by the equation <span><math><mi>f</mi><mo>=</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>3</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></msubsup></math></span> for a weight triple <span><math><mo>(</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span>, as well as the category of coherent sheaves over the weighted projective line <span><math><mi>X</mi></math></span> defined by <em>f</em>. We calculate Hall polynomials associated with extension bundles, line bundles and torsion sheaves over <span><math><mi>X</mi></math></span>. By using derived equivalence, this provides a unified conceptual method for calculating Hall polynomials for representations of tame quivers obtained by Szántó and Szöllősi (2024) <span><span>[35]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108157"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145739259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108151
Barbara Gatti , Gioia Schulte
In the study of algebraic curves with many points over a finite field, a well known general problem is to understand better the properties of -maximal curves whose genera fall in the higher part of the spectrum of the genera of all -maximal curves. This problem is still open for genera smaller than . In this paper we consider the case of where and the curve is the Galois subcover of the Hermitian curve w.r.t. a cyclic automorphism group of order 4. Our contributions concern Frobenius embedding, Weierstrass semigroups and automorphism groups.
{"title":"On a Galois subcover of the Hermitian curve of genus g=18(q−1)2","authors":"Barbara Gatti , Gioia Schulte","doi":"10.1016/j.jpaa.2025.108151","DOIUrl":"10.1016/j.jpaa.2025.108151","url":null,"abstract":"<div><div>In the study of algebraic curves with many points over a finite field, a well known general problem is to understand better the properties of <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span>-maximal curves whose genera fall in the higher part of the spectrum of the genera of all <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span>-maximal curves. This problem is still open for genera smaller than <span><math><mo>⌊</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>(</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>q</mi><mo>+</mo><mn>4</mn><mo>)</mo><mo>⌋</mo></math></span>. In this paper we consider the case of <span><math><mi>g</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>8</mn></mrow></mfrac><msup><mrow><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> where <span><math><mi>q</mi><mo>≡</mo><mn>1</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>4</mn><mo>)</mo></math></span> and the curve is the Galois subcover of the Hermitian curve w.r.t. a cyclic automorphism group of order 4. Our contributions concern Frobenius embedding, Weierstrass semigroups and automorphism groups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108151"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108156
Emile Bouaziz
We write down an explicit operator on the chiral de Rham complex of a Calabi-Yau variety X which intertwines the usual module structure with its twist by the spectral flow automorphism of the , producing the expected spectral flow equivariance. Taking the trace of the operators and on cohomology, and using the obvious interaction of spectral flow with characters, we obtain an explicit categorification of ellipticity of the elliptic genus of X, which is well known by other means.
{"title":"Spectral flow equivariance for Calabi-Yau Sigma models","authors":"Emile Bouaziz","doi":"10.1016/j.jpaa.2025.108156","DOIUrl":"10.1016/j.jpaa.2025.108156","url":null,"abstract":"<div><div>We write down an explicit operator on the chiral de Rham complex of a Calabi-Yau variety <em>X</em> which intertwines the usual <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span> module structure with its twist by the spectral flow automorphism of the <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span>, producing the expected <em>spectral flow equivariance</em>. Taking the trace of the operators <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>J</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> on cohomology, and using the obvious interaction of spectral flow with characters, we obtain an explicit categorification of ellipticity of the elliptic genus of <em>X</em>, which is well known by other means.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108156"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a new technique to describe partial reductions and inverse Hamiltonian reductions between affine -algebras along the closure relations of associated nilpotent orbits in the case of , fulfilling all the missing constructions in the literature. We also apply the partial reductions to modules in the Kazhdan–Lusztig category and show compatibility with the usual reductions of Weyl modules.
{"title":"Connecting affine W-algebras: A case study on sl4","authors":"Justine Fasquel , Zachary Fehily , Ethan Fursman , Shigenori Nakatsuka","doi":"10.1016/j.jpaa.2025.108149","DOIUrl":"10.1016/j.jpaa.2025.108149","url":null,"abstract":"<div><div>We introduce a new technique to describe partial reductions and inverse Hamiltonian reductions between affine <span><math><mi>W</mi></math></span>-algebras along the closure relations of associated nilpotent orbits in the case of <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>, fulfilling all the missing constructions in the literature. We also apply the partial reductions to modules in the Kazhdan–Lusztig category and show compatibility with the usual reductions of Weyl modules.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108149"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108154
Taito Shimoji
Let Γ be a lattice in a simply-connected nilpotent Lie group N whose Lie algebra is p-filiform. We show that Γ is either abelian or 2-step nilpotent if Γ is isomorphic to the fundamental group of a smooth complex algebraic variety. Moreover as an application of our result, we give a required condition of a lattice in a simply-connected nilpotent Lie group of dimension less than or equal to six to be isomorphic to the fundamental group of a smooth complex algebraic variety.
{"title":"Gradings on nilpotent Lie algebras associated with the nilpotent fundamental groups of smooth complex algebraic varieties","authors":"Taito Shimoji","doi":"10.1016/j.jpaa.2025.108154","DOIUrl":"10.1016/j.jpaa.2025.108154","url":null,"abstract":"<div><div>Let Γ be a lattice in a simply-connected nilpotent Lie group <em>N</em> whose Lie algebra <span><math><mi>n</mi></math></span> is <em>p</em>-filiform. We show that Γ is either abelian or 2-step nilpotent if Γ is isomorphic to the fundamental group of a smooth complex algebraic variety. Moreover as an application of our result, we give a required condition of a lattice in a simply-connected nilpotent Lie group of dimension less than or equal to six to be isomorphic to the fundamental group of a smooth complex algebraic variety.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108154"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108150
Klaus Mattis, Timo Weiß
For an endofunctor on an (∞-)category we define the ∞-category of generalized Cartier modules as the lax equalizer of F and the identity. This generalizes the notion of Cartier modules on -schemes considered in [4]. We show that in favorable cases is monadic over . If is a Grothendieck abelian category and is an exact and colimit-preserving endofunctor, we use this fact to construct an equivalence of stable ∞-categories. We use this equivalence to construct a perverse t-structure on for any Noetherian -scheme X with absolute Frobenius F. If F is finite, this coincides with the perverse t-structure constructed in [3].
{"title":"The derived ∞-category of Cartier modules","authors":"Klaus Mattis, Timo Weiß","doi":"10.1016/j.jpaa.2025.108150","DOIUrl":"10.1016/j.jpaa.2025.108150","url":null,"abstract":"<div><div>For an endofunctor <span><math><mi>F</mi><mo>:</mo><mi>C</mi><mo>→</mo><mi>C</mi></math></span> on an (∞-)category <span><math><mi>C</mi></math></span> we define the ∞-category <span><math><mi>Cart</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> of generalized Cartier modules as the lax equalizer of <em>F</em> and the identity. This generalizes the notion of Cartier modules on <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-schemes considered in <span><span>[4]</span></span>. We show that in favorable cases <span><math><mi>Cart</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> is monadic over <span><math><mi>C</mi></math></span>. If <span><math><mi>A</mi></math></span> is a Grothendieck abelian category and <span><math><mi>F</mi><mo>:</mo><mi>A</mi><mo>→</mo><mi>A</mi></math></span> is an exact and colimit-preserving endofunctor, we use this fact to construct an equivalence <span><math><mi>D</mi><mo>(</mo><mi>Cart</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>F</mi><mo>)</mo><mo>)</mo><mo>≃</mo><mi>Cart</mi><mo>(</mo><mi>D</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>,</mo><mi>D</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>)</mo></math></span> of stable ∞-categories. We use this equivalence to construct a perverse t-structure on <span><math><mi>D</mi><mo>(</mo><mi>Cart</mi><mo>(</mo><mi>Mod</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>)</mo><mo>)</mo></math></span> for any Noetherian <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-scheme <em>X</em> with absolute Frobenius <em>F</em>. If <em>F</em> is finite, this coincides with the perverse t-structure constructed in <span><span>[3]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108150"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145739260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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