We show that the simplicial stratification associated to a triangulation of a PL pseudomanifold possesses a canonical system of trivializations of link bundles that satisfies a natural compatibility condition over nested singular strata. Consequently, Agustín Vicente and Fernández de Bobadilla’s generalization of Banagl’s intersection space construction is applicable to all PL pseudomanifolds (and in particular, to all complex algebraic varieties).
我们证明了与PL伪流形三角剖分相关的简单分层具有满足嵌套奇异层上自然相容条件的连接束平凡化的规范系统。因此，Agustín Vicente和Fernández de Bobadilla对Banagl交空间构造的推广适用于所有PL伪泛形(特别是所有复代数变体)。
{"title":"A short note on simplicial stratifications","authors":"Dominik J. Wrazidlo","doi":"10.1090/bproc/168","DOIUrl":"https://doi.org/10.1090/bproc/168","url":null,"abstract":"We show that the simplicial stratification associated to a triangulation of a PL pseudomanifold possesses a canonical system of trivializations of link bundles that satisfies a natural compatibility condition over nested singular strata. Consequently, Agustín Vicente and Fernández de Bobadilla’s generalization of Banagl’s intersection space construction is applicable to all PL pseudomanifolds (and in particular, to all complex algebraic varieties).","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115751758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Errata to “contravariant forms on Whittaker modules”","authors":"Adam Brown, A. Romanov","doi":"10.1090/bproc/145","DOIUrl":"https://doi.org/10.1090/bproc/145","url":null,"abstract":"Here we make corrections to address a false statement by Brown and Romanov [Proc. Amer. Math. Soc. 149 (2021), pp. 37–52].","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127440601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. These functions appear in various fields of science and technology, in particular they were discovered in quantum mechanics in the context of weak values introduced by Y. Aharonov and collaborators. The evolution problem of superoscillatory functions as initial conditions for the Schrödinger equation is intensively studied nowadays and the supershift property of the solution of Schrödinger equation encodes the persistence of superoscillatory phenomenon during the evolution. In this paper, we prove that the evolution of a superoscillatory initial datum for spinning particles in a magnetic field has the supershift property. Our techniques are based on the exact propagator of spinning particles, the associated infinite order differential operators and their continuity on suitable spaces of entire functions with growth conditions.
{"title":"Evolution of superoscillations for spinning particles","authors":"F. Colombo, Elodie Pozzi, I. Sabadini, B. Wick","doi":"10.1090/bproc/159","DOIUrl":"https://doi.org/10.1090/bproc/159","url":null,"abstract":"Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. These functions appear in various fields of science and technology, in particular they were discovered in quantum mechanics in the context of weak values introduced by Y. Aharonov and collaborators. The evolution problem of superoscillatory functions as initial conditions for the Schrödinger equation is intensively studied nowadays and the supershift property of the solution of Schrödinger equation encodes the persistence of superoscillatory phenomenon during the evolution. In this paper, we prove that the evolution of a superoscillatory initial datum for spinning particles in a magnetic field has the supershift property. Our techniques are based on the exact propagator of spinning particles, the associated infinite order differential operators and their continuity on suitable spaces of entire functions with growth conditions.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131733754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that the Carathéodory space of place functions on the free product of two Boolean algebras is Riesz isomorphic with Fremlin’s Archimedean Riesz space tensor product of their respective Carathéodory spaces of place functions. We provide a solution to Fremlin’s problem 315Y(f) [Measure Theory, Torres Fremlin, Colchester, 2004] concerning completeness in the free product of Boolean algebras by applying our results on the Archimedean Riesz space tensor product to Carathéodory spaces of place functions.
{"title":"On the Boolean algebra tensor product via Carathéodory spaces of place functions","authors":"G. Buskes, Page Thorn","doi":"10.1090/bproc/161","DOIUrl":"https://doi.org/10.1090/bproc/161","url":null,"abstract":"We show that the Carathéodory space of place functions on the free product of two Boolean algebras is Riesz isomorphic with Fremlin’s Archimedean Riesz space tensor product of their respective Carathéodory spaces of place functions. We provide a solution to Fremlin’s problem 315Y(f) [Measure Theory, Torres Fremlin, Colchester, 2004] concerning completeness in the free product of Boolean algebras by applying our results on the Archimedean Riesz space tensor product to Carathéodory spaces of place functions.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132449514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We describe the distribution of infinite groups within the RO(G)RO(G)-graded stable homotopy groups of spheres for a finite group GG.
讨论了有限群G G的RO(G) RO(G)梯度稳定同伦群中无限群的分布。
{"title":"Ranks of 𝑅𝑂(𝐺)-graded stable homotopy groups of spheres for finite groups 𝐺","authors":"J. Greenlees, J. Quigley","doi":"10.1090/bproc/140","DOIUrl":"https://doi.org/10.1090/bproc/140","url":null,"abstract":"<p>We describe the distribution of infinite groups within the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R upper O left-parenthesis upper G right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>R</mml:mi>\u0000 <mml:mi>O</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">RO(G)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-graded stable homotopy groups of spheres for a finite group <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126698526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We generalize Krust’s theorem to an anisotropic setting by showing the following. If Σ Sigma is an anisotropic minimal surface in an axially symmetric normed linear space which is a graph over a convex domain contained in a plane orthogonal to the axis of symmetry, then its conjugate anisotropic minimal surface must also be a graph. We also generalize a reflection principle of Lawson relating symmetries of an anisotropic minimal surface with symmetries of its conjugate surface.
{"title":"A version of Krust’s theorem for anisotropic minimal surfaces","authors":"B. Palmer","doi":"10.1090/bproc/151","DOIUrl":"https://doi.org/10.1090/bproc/151","url":null,"abstract":"We generalize Krust’s theorem to an anisotropic setting by showing the following. If \u0000\u0000 \u0000 Σ\u0000 Sigma\u0000 \u0000\u0000 is an anisotropic minimal surface in an axially symmetric normed linear space which is a graph over a convex domain contained in a plane orthogonal to the axis of symmetry, then its conjugate anisotropic minimal surface must also be a graph.\u0000\u0000We also generalize a reflection principle of Lawson relating symmetries of an anisotropic minimal surface with symmetries of its conjugate surface.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133807325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let GG be a finite simple graph and let IGI_G denote its associated toric ideal in the polynomial ring RR. For each integer n≥2ngeq 2, we completely determine all the possible values for the tuple (reg(R/IG),deg(hR/I
{"title":"Comparing invariants of toric ideals of bipartite graphs","authors":"K. Bhaskara, A. Tuyl","doi":"10.1090/bproc/174","DOIUrl":"https://doi.org/10.1090/bproc/174","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be a finite simple graph and let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I Subscript upper G\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:mi>G</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">I_G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> denote its associated toric ideal in the polynomial ring <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\">\u0000 <mml:semantics>\u0000 <mml:mi>R</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">R</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. For each integer <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n greater-than-or-equal-to 2\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>≥<!-- ≥ --></mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ngeq 2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, we completely determine all the possible values for the tuple <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis r e g left-parenthesis upper R slash upper I Subscript upper G Baseline right-parenthesis comma degree left-parenthesis h Subscript upper R slash upper I Sub Subscript upper G Subscript Baseline left-parenthesis t right-parenthesis right-parenthesis comma p d i m left-parenthesis upper R slash upper I Subscript upper G Baseline right-parenthesis comma d e p t h left-parenthesis upper R slash upper I Subscript upper G Baseline right-parenthesis comma dimension left-parenthesis upper R slash upper I Subscript upper G Baseline right-parenthesis right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>reg</mml:mi>\u0000 <mml:mo><!-- --></mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>R</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>/</mml:mo>\u0000 </mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:mi>G</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>deg</mml:mi>\u0000 <mml:mo><!-- --></mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>h</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>R</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>/</mml:mo>\u0000 </mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>I</mml:mi>\u0000 ","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125020347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Grushin sphere is an almost-Riemannian manifold that degenerates along its equator. We construct a sequence of Riemannian metrics on a sphere Sm+nS^{m+n} with Ric≥1Ricge 1 such that its Gromov-Hausdorff limit is the nn-dimensional Grushin hemisphere.
{"title":"The Grushin hemisphere as a Ricci limit space with curvature ≥1","authors":"Jiayin Pan","doi":"10.1090/bproc/160","DOIUrl":"https://doi.org/10.1090/bproc/160","url":null,"abstract":"<p>The Grushin sphere is an almost-Riemannian manifold that degenerates along its equator. We construct a sequence of Riemannian metrics on a sphere <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S Superscript m plus n\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>m</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">S^{m+n}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> with <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R i c greater-than-or-equal-to 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>R</mml:mi>\u0000 <mml:mi>i</mml:mi>\u0000 <mml:mi>c</mml:mi>\u0000 <mml:mo>≥<!-- ≥ --></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Ricge 1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> such that its Gromov-Hausdorff limit is the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\">\u0000 <mml:semantics>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-dimensional Grushin hemisphere.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114828455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove that a family of links, which includes all special alternating knots, does not admit non-nugatory crossing changes which preserve the isotopy type of the link. Our proof incorporates a result of Lidman and Moore [Trans. Amer. Math. Soc. 369 (2017), pp. 3639–3654] on crossing changes to knots with L L -space branched double-covers, as well as tools from Scharlemann and Thompson’s [Comment. Math. Helv. 64 (1989), pp. 527–535] proof of the cosmetic crossing conjecture for the unknot.
我们证明了包含所有特殊交变结的连杆族不允许保留其同位素类型的非核交叉变化。我们的证明结合了Lidman和Moore[译]的结果。阿米尔。数学。Soc. 369 (2017)， pp. 3639-3654]关于L - L空间分支双盖的交叉变化结，以及Scharlemann和Thompson的工具[评论]。数学。[Helv. 64 (1989)， pp. 527-535]解结的表面交叉猜想的证明。
{"title":"On the cosmetic crossing conjecture for special alternating links","authors":"Joseph Boninger","doi":"10.1090/bproc/184","DOIUrl":"https://doi.org/10.1090/bproc/184","url":null,"abstract":"We prove that a family of links, which includes all special alternating knots, does not admit non-nugatory crossing changes which preserve the isotopy type of the link. Our proof incorporates a result of Lidman and Moore [Trans. Amer. Math. Soc. 369 (2017), pp. 3639–3654] on crossing changes to knots with \u0000\u0000 \u0000 L\u0000 L\u0000 \u0000\u0000-space branched double-covers, as well as tools from Scharlemann and Thompson’s [Comment. Math. Helv. 64 (1989), pp. 527–535] proof of the cosmetic crossing conjecture for the unknot.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125905215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that for certain non-CM elliptic curves E/QE_{/mathbb {Q}} such that 33 is an Eisenstein prime of good reduction, a positive proportion of the quadratic twists EψE_{psi } of EE have Mordell–Weil rank one and the 33-adic height pairing on Eψ(Q)E_{psi }(mathbb {Q}) is non-degenerate. We also show similar but weaker results for other Eisenstein primes. The method of proof also yields examples of middle cod
{"title":"A note on rank one quadratic twists of elliptic curves and the non-degeneracy of 𝑝-adic regulators at Eisenstein primes","authors":"Ashay A. Burungale, C. Skinner","doi":"10.1090/bproc/144","DOIUrl":"https://doi.org/10.1090/bproc/144","url":null,"abstract":"<p>We show that for certain non-CM elliptic curves <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E Subscript slash double-struck upper Q\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>E</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>/</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Q</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">E_{/mathbb {Q}}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> such that <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is an Eisenstein prime of good reduction, a positive proportion of the quadratic twists <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E Subscript psi\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>E</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>ψ<!-- ψ --></mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">E_{psi }</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E\">\u0000 <mml:semantics>\u0000 <mml:mi>E</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">E</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> have Mordell–Weil rank one <italic>and</italic> the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-adic height pairing on <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E Subscript psi Baseline left-parenthesis double-struck upper Q right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>E</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>ψ<!-- ψ --></mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Q</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">E_{psi }(mathbb {Q})</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is non-degenerate. We also show similar but weaker results for other Eisenstein primes. The method of proof also yields examples of middle cod","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127607222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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