Tate shafarevich group

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August undefined, 2024

WebRIMS Kôkyûroku Bessatsu B32 (2012), 51−60 The p‐parts of Tate‐Shafarevich Groups of Elliptic Curves Dedicated to Takeshi Tsuji By Florian E. Ito SPRUNG* Abstract We give an overview of Iwasawa theory for elliptic curves, and what this theory can tell us about the size of the Tate‐Shafarevich group in towers of number fields. What is new is that we … WebThe Tate–Shafarevich group of an abelian variety A defined over a number field K consists of the elements of the Weil–Châtelet group that become trivial in all of the completions of …

eLibM – Doc. Math. 25, 2445-2471 (2024)

Webpothesis and the ﬁniteness of Tate–Shafarevich groups of elliptic curves. Várilly-Alvarado and Viray show this in [VAV] (see Theorem 5.3) in applying a deep theorem of Witten-berg [Wi2, Théorème 1.1] (see also [Wi1]) on genus 1 ﬁbrations. Y →. P. 1, and checking that the conditions of his theorem are satisﬁed. WebOct 4, 2024 · In this note, we prove a duality theorem for the Tate–Shafarevich group of a finite discrete Galois module over the function field K of a curve over an algebraically closed field: there is a perfect duality of finite groups for F a finite étale Galois module on K of order invertible in K and with $F' = {{\mathrm{Hom}}}(F,\mathbf{Q}/\mathbf {Z}(1))$. shoe fetch

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WebNov 4, 2024 · Within the Tate–Shafarevich group of an elliptic curve E defined over a number field K, there is a canonical subgroup defined by imposing stronger conditions at the places above a given prime p. WebJan 1, 2007 · The fine Tate–Shafarevich group. Abstract Within the Tate–Shafarevich group of an elliptic curve E defined over a number field K, there is a canonical subgroup defined … WebTexts with language specifed as french OR fre shoe fest 2023

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WebMar 29, 2024 · DOI: 10.2140/ant.2024.15.627 Corpus ID: 90259689; Elements of given order in Tate–Shafarevich groups of abelian varieties in quadratic twist families @article{Bhargava2024ElementsOG, title={Elements of given order in Tate–Shafarevich groups of abelian varieties in quadratic twist families}, author={Manjul Bhargava and Zev … Web1. Mordell-Weil group, rank, and Tate-Shafarevich group An elliptic curve Eover a eld Kis a smooth projective curve that has an a ne equation of the form y2 + a 1xy+ a 3y= x3 + a … shoe fetish researchWebConjecture 1. (Shafarevich and Tate) The group X(E=Q) is nite. These two invariants, the rank rand the Tate-Shafarevich group X(E=Q), are encoded in the Selmer groups of E. Fix a prime p, and let E(p) denote the Gal(Q =Q)-module of all torsion points of Ewhose orders are powers of p. The Selmer group S p(E=Q) is de ned by the following exact ... shoe festival payless

"WebSep 19, 2024 · In this section we apply the theory we developed to concrete examples, and construct elements of p-torsion subgroups of Tate–Shafarevich groups, for $p \le 11$ an odd prime. As mentioned in the introduction, these computations are of the most interest when the prime p is at least 7, since for $p \le 5$ the usual method of p -descent works … " - Tate shafarevich group

Tate shafarevich group

WebTheorem 1.1. Let E=Q be an elliptic curve whose Tate-Shafarevich group X(E=Q) has nite p-primary part. Suppose that the p-adic height on the ne Selmer group is non-degenerate. Then there is an injection with nite cokernel J of R(E=Q) into the cokernel of the corestriction map cor: lim pn n H1(G ( Q);TpE) ˜H1(G (Q);T E): WebNow we can deﬁne the Selmer group and the Tate-Shafarevich group. Deﬁnition 1.1 (Selmer group). The Selmer group, denoted S(n)(E=K) is deﬁned by S(n)(E=K) = ker H1(G K;E[n]) ! Y v H1(G K v;E)!: 2. Mordell-Weil Deﬁnition1.2 (Tate-Shafarevichgroup). TheTate-Shafarevichgroup,denotedX(E=K),isde-ﬁned by X(E=K) = ker

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WebJan 8, 2024 · Tate's conjecture and the Tate-Shafarevich group over global function fields. Thomas H. Geisser. Let be a regular variety, flat and proper over a complete regular curve …

WebLei and M. F. Lim, Mordell-Weil ranks and Tate-Shafarevich groups of elliptic curves with mixed-reduction type over cyclotomic extensions. Preprint 2024. arxiv 1911.10643. 25. A. Lei and G. Ponisnet, On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions. Proc. Amer. Math. WebDescription: Let p p be a prime and S S a finite p p-group. A p p-fusion system on S S is a category whose objects are the subgroups of S and whose morphisms are certain injective group homomorphisms. Fusion systems are of interest in modular representation theory, algebraic topology, and local finite group theory.

WebWithin the Tate-Shafarevich group of an elliptic curve E de ned over a number eld K, there is a canonical subgroup de ned by imposing stronger conditions at the places above a given … http://virtualmath1.stanford.edu/~conrad/BSDseminar/Notes/L3.pdf

WebVISIBILITY OF TATE-SHAFAREVICH GROUPS TOM FISHER Abstract. These are the notes for a short course given at the University of Warwick on 29th and 30th April 2008. 1. Weil-Chˆatelet groups Let Abe an abelian variety over a ﬁeld Kof characteristic 0. Let K be the algebraic closure of K, and let L/Kbe any ﬁeld extension. Deﬁnition 1.1.

Webthe Shafarevich–Tate group of an elliptic curve E over a number ﬁeld K. We are speciﬁcally interested in cases where the elliptic curves are deﬁned over the rationals, and are subabelian vari-eties of the new part of the jacobian of a modular curve (specif-0(N), where N is the conductor of the elliptic curve). shoe fetish meaningWebApr 12, 2012 · The result also implies that the mean value of the 2-rank of the corresponding Tate–Shafarevich groups for square-free positive integers n ≤ X is as X → ∞. This is quite … race to 5 points bet meaningWebThe Mordell{Weil group EpFq, the p8-Selmer group Sel p8pE{Fqand the p-primary part of Tate{Shafarevich group X pE{Fqrp8sare related by the following exact sequence: 0 ÑEpFqbQ p{Z pÑSel p8pE{FqÑX pE{Fqrp8sÑ0: This sequence may be called the p8-descent of E{F. Then we have an in-equality 0 ⁄r MWpE{Fq⁄r ppE{Fq; where the equality r MWpE{Fq r shoe festivalWebTate–Shafarevich group of Jacobian of Selmer curve 3 X 3 + 4 Y 3 + 5 Z 3 = 0. C / Q: 3 X 3 + 4 Y 3 + 5 Z 3 = 0 is known to be a nontrivial element of the Tate–Shafarevich group of the … shoe fetageWebThe Tate-Shafarevich group associated to an elliptic curve. If E is an elliptic curve over a global field K, the Tate-Shafarevich group is the subgroup of elements in H 1 ( K, E) which … shoe figurines collectiblesWebAs a preliminary remark, note that the Tate-Shafarevich group also measures a certain defect, just like the class group. Its elements correspond to homogeneous spaces that … race to 5 pointsWebDans cet article on formule les conjectures d’Isogenie, de Mumford-Tate et de Shafarevich généralisées et on démontre qu’elles sont équivalentes. shoeffield medical facility in tonawanda