Tate-shafarevich group
WebMay 20, 2024 · Rubin, Tate-Shafarevich gr oups of elliptic curves with complex multiplication, Adv anced Studies in Pure Mathematics 17 , 1989, Algebraic Number … WebProof of Theorem 1.1. If Tate’s conjecture holds for X and the Tate-Shafarevich ∗ group of AlbX is finite, then (T Br(X )) vanishes by Theorem 1.3. But the Brauer group is torsion …
Tate-shafarevich group
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WebFeb 9, 2016 · Martin L. Brown. The structure of the Tate-Shafarevich groups of a class of elliptic curves over global function fields is determined. These are known to be finite … WebWe first study the 3-adic valuation of the algebraic part of the value of the Hasse–Weil L-function L (C N, s) of C N over ℚ at s = 1, and we exhibit a relation between the 3-part of its …
WebJun 16, 2024 · RECENT PROGRESS ON THE TATE CONJECTURE 577 More precisely, the class of a subvariety Y of X lies in the subgroup of H2a(X,Z l(a)) fixed by the Galois 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. …
WebJun 5, 2012 · LMSST: 24 Lectures on Elliptic Curves - November 1991. To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. WebNow assume G is a commutative group scheme over K. We define the Tate– Shafarevich groups of G relative to C by Xi C(G) := Ker(Hi(K,G) → Y c∈C(1) Hi(K c,G)) for each i ≥ 0. The …
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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 … trendnet south africaWebON THE p-PRIMARY PART OF TATE-SHAFAREVICH GROUP 409 2. Iwawawa theory for a supersingular prime In this section, we recall the Iwasawa theory of E at a supersingular … trendnet security cameraWebRELATING THE TATE–SHAFAREVICH GROUP OF AN ELLIPTIC CURVE 205 We begin with a well-known lemma, stated without proof. Lemma 2.1. Let G be a group operating on a … trendnet switch configWebTate–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 … trendnet switch factory resetWebThe Tate--Shafarevich group of A is a torsion group, and so is the union of its m -torsion subgroups, as m ranges over integers ≥ 1. In fact the same is true of the Weil--Chatelet … trendnet switch firmwareWebIgor Rostislavovich Shafarevich (Russian: И́горь Ростисла́вович Шафаре́вич; 3 June 1923 – 19 February 2024) was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic … temple university campus safety servicesWebDipendra Prasad IIT Bombay (Report on joint work with Sudhanshu Shekhar) Relating the Tate-Shafarevich group of an Elliptic curve with the class group. An example of Harder … temple university car flip