Pub Date : 2026-01-01Epub Date: 2025-12-02DOI: 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 : 2026-01-01Epub Date: 2025-12-08DOI: 10.1016/j.jpaa.2025.108152
Benjamin Katz, Andrew J. Soto Levins
This work concerns an Ext analog of the classical Euler characteristic of a pair of finitely generated modules over commutative noetherian local rings.
本文研究了交换诺瑟局部环上一对有限生成模的经典欧拉特征的Ext模拟。
{"title":"On the ext analog of the Euler characteristic","authors":"Benjamin Katz, Andrew J. Soto Levins","doi":"10.1016/j.jpaa.2025.108152","DOIUrl":"10.1016/j.jpaa.2025.108152","url":null,"abstract":"<div><div>This work concerns an Ext analog of the classical Euler characteristic of a pair of finitely generated modules over commutative noetherian local rings.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108152"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705834","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 : 2026-01-01Epub 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":"2026-01-01","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}
Pub Date : 2026-01-01Epub Date: 2025-12-22DOI: 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 : 2026-01-01Epub Date: 2025-12-08DOI: 10.1016/j.jpaa.2025.108147
Aranya Lahiri , Claus Sorensen , Matthias Strauch
Let be a p-saturated group and a complete and discretely valued extension. In this paper we introduce the space of K-valued overconvergent functions . In the process we promote the rigid analytic group attached to in [13] to a dagger group. A main result of this article is that under certain assumptions (satisfied for example when G is a uniform pro-p group) the distribution algebra , i.e. the strong dual of , is a Fréchet-Stein algebra in the sense of [21].
In the last section we introduce overconvergent representations and show that there is an anti-equivalence of categories between overconvergent G-representations of compact type and continuous -modules on nuclear Fréchet spaces. This is analogous to the anti-equivalence between locally analytic representations and modules over the locally analytic distribution algebra as proved in [20].
{"title":"Dagger groups and p-adic distribution algebras","authors":"Aranya Lahiri , Claus Sorensen , Matthias Strauch","doi":"10.1016/j.jpaa.2025.108147","DOIUrl":"10.1016/j.jpaa.2025.108147","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> be a <em>p</em>-saturated group and <span><math><mi>K</mi><mo>/</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> a complete and discretely valued extension. In this paper we introduce the space of <em>K</em>-valued <em>overconvergent</em> functions <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>. In the process we promote the rigid analytic group attached to <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> in <span><span>[13]</span></span> to a dagger group. A main result of this article is that under certain assumptions (satisfied for example when <em>G</em> is a uniform pro-<em>p</em> group) the distribution algebra <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>, i.e. the strong dual of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>, is a Fréchet-Stein algebra in the sense of <span><span>[21]</span></span>.</div><div>In the last section we introduce overconvergent representations and show that there is an anti-equivalence of categories between overconvergent <em>G</em>-representations of compact type and continuous <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>-modules on nuclear Fréchet spaces. This is analogous to the anti-equivalence between locally analytic representations and modules over the locally analytic distribution algebra as proved in <span><span>[20]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108147"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841224","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 : 2025-12-01Epub Date: 2025-11-14DOI: 10.1016/j.jpaa.2025.108133
Ihechukwu Chinyere , Martin Edjvet , Gerald Williams
We consider the cyclically presented groups defined by cyclic presentations with 2m generators whose relators are the 2m positive length three relators . We show that they are hyperbolic if and only if . This completes the classification of the hyperbolic cyclically presented groups with positive length three relators.
{"title":"All hyperbolic cyclically presented groups with positive length three relators","authors":"Ihechukwu Chinyere , Martin Edjvet , Gerald Williams","doi":"10.1016/j.jpaa.2025.108133","DOIUrl":"10.1016/j.jpaa.2025.108133","url":null,"abstract":"<div><div>We consider the cyclically presented groups defined by cyclic presentations with 2<em>m</em> generators <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> whose relators are the 2<em>m</em> positive length three relators <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>+</mo><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span>. We show that they are hyperbolic if and only if <span><math><mi>m</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>}</mo></math></span>. This completes the classification of the hyperbolic cyclically presented groups with positive length three relators.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108133"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693704","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 : 2025-12-01Epub Date: 2025-10-27DOI: 10.1016/j.jpaa.2025.108119
Victor Carmona
This work addresses the homotopical analysis of enveloping operads in a general cofibrantly generated symmetric monoidal model category. We show the potential of this analysis by obtaining, in a uniform way, several central results regarding the homotopy theory of operadic algebras.
{"title":"Enveloping operads and applications","authors":"Victor Carmona","doi":"10.1016/j.jpaa.2025.108119","DOIUrl":"10.1016/j.jpaa.2025.108119","url":null,"abstract":"<div><div>This work addresses the homotopical analysis of enveloping operads in a general cofibrantly generated symmetric monoidal model category. We show the potential of this analysis by obtaining, in a uniform way, several central results regarding the homotopy theory of operadic algebras.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108119"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145384599","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 : 2025-12-01Epub Date: 2025-11-10DOI: 10.1016/j.jpaa.2025.108128
Agata Smoktunowicz
This paper presents an extension of the classical method [1] for associating groups to pre-Lie rings. This enhancement will hopefully help us to better understand an object used to investigate set-theoretic solutions of the Yang-Baxter equation and Hopf-Galois extensions called a brace. We also show that some classes of braces of cardinality with p prime and n larger than p can be obtained with our extension.
{"title":"An extension of the group of flows method for finite pre-Lie rings","authors":"Agata Smoktunowicz","doi":"10.1016/j.jpaa.2025.108128","DOIUrl":"10.1016/j.jpaa.2025.108128","url":null,"abstract":"<div><div>This paper presents an extension of the classical method <span><span>[1]</span></span> for associating groups to pre-Lie rings. This enhancement will hopefully help us to better understand an object used to investigate set-theoretic solutions of the Yang-Baxter equation and Hopf-Galois extensions called a brace. We also show that some classes of braces of cardinality <span><math><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <em>p</em> prime and <em>n</em> larger than <em>p</em> can be obtained with our extension.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108128"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528932","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 : 2025-12-01Epub Date: 2025-11-10DOI: 10.1016/j.jpaa.2025.108129
Lucas Hamada, Kazuki Kato, Ryo Komiya
This paper investigates a Tate algebra version of the Jacobian conjecture, referred to as the Tate-Jacobian conjecture, for commutative rings R equipped with an I-adic topology. We show that if the I-adic topology on R is Hausdorff and is a subring of a -algebra, then the Tate-Jacobian conjecture is equivalent to the Jacobian conjecture. Conversely, if has positive characteristic, the Tate-Jacobian conjecture fails. Furthermore, we establish that the Jacobian conjecture for is equivalent to the following statement: for all but finitely many primes p, the inverse of a polynomial map over whose Jacobian determinant is an element of lies in the Tate algebra over .
{"title":"A Tate algebra version of the Jacobian conjecture","authors":"Lucas Hamada, Kazuki Kato, Ryo Komiya","doi":"10.1016/j.jpaa.2025.108129","DOIUrl":"10.1016/j.jpaa.2025.108129","url":null,"abstract":"<div><div>This paper investigates a Tate algebra version of the Jacobian conjecture, referred to as <em>the Tate-Jacobian conjecture</em>, for commutative rings <em>R</em> equipped with an <em>I</em>-adic topology. We show that if the <em>I</em>-adic topology on <em>R</em> is Hausdorff and <span><math><mi>R</mi><mo>/</mo><mi>I</mi></math></span> is a subring of a <span><math><mi>Q</mi></math></span>-algebra, then the Tate-Jacobian conjecture is equivalent to the Jacobian conjecture. Conversely, if <span><math><mi>R</mi><mo>/</mo><mi>I</mi></math></span> has positive characteristic, the Tate-Jacobian conjecture fails. Furthermore, we establish that the Jacobian conjecture for <span><math><mi>C</mi></math></span> is equivalent to the following statement: for all but finitely many primes <em>p</em>, the inverse of a polynomial map over <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> whose Jacobian determinant is an element of <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow><mrow><mo>×</mo></mrow></msubsup></math></span> lies in the Tate algebra over <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108129"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528933","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 : 2025-12-01Epub Date: 2025-11-07DOI: 10.1016/j.jpaa.2025.108127
Dmitriy Voloshyn
We study birational quasi-isomorphisms between normal Noetherian domains endowed with cluster structures of geometric type. We prove an analogue of the Starfish lemma that allows one to transfer various cluster and algebraic properties of one variety onto another. In particular, we develop tools for proving that an upper cluster algebra equals the given commutative ring.
{"title":"Starfish lemma via birational quasi-isomorphisms","authors":"Dmitriy Voloshyn","doi":"10.1016/j.jpaa.2025.108127","DOIUrl":"10.1016/j.jpaa.2025.108127","url":null,"abstract":"<div><div>We study birational quasi-isomorphisms between normal Noetherian domains endowed with cluster structures of geometric type. We prove an analogue of the Starfish lemma that allows one to transfer various cluster and algebraic properties of one variety onto another. In particular, we develop tools for proving that an upper cluster algebra equals the given commutative ring.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108127"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528934","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号