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Tate-shafarevich group

WebFeb 12, 2007 · 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 … WebTate-Shafarevich groups, regulators of elliptic curves and L-functions Christophe Delaunay. Notations Let Ebe an elliptic curve defined Q with conductor N: E : y2 = x3 + Ax+ B Let …

Tate-Shafarevich groups, regulators of elliptic curves and L …

WebBrauer Groups and Tate-Shafarevich Groups 393 where T 2 and T 3 are finite groups of order δ. In particular, if one of W(A) or Br(X) is finite, then so is the other, and their orders … WebMay 20, 2024 · Rubin, Tate-Shafarevich gr oups of elliptic curves with complex multiplication, Adv anced Studies in Pure Mathematics 17 , 1989, Algebraic Number … rae nave https://sanda-smartpower.com

Reductions of an Elliptic Curve and their Tate-Shafarevich Groups.

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 … WebConjecture 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 ... 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 … raena torane

Brauer Groups and Tate-Shafarevich Groups - 東京大学

Category:The growth of Tate–Shafarevich groups in cyclic extensions

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Tate-shafarevich group

Reductions of an Elliptic Curve and their Tate-Shafarevich Groups.

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 … 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 …

Tate-shafarevich group

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WebDec 18, 2024 · Thomas Geisser. We give a formula relating the order of the Brauer group of a surface fibered over a curve over a finite field to the order of the Tate-Shafarevich group of the Jacobian of the generic fiber. The formula implies that the Brauer group of a smooth and proper surface over a finite field is a square if it is finite. WebThe Tate–Shafarevich conjecture states that the Tate–Shafarevich group is finite. Rubin ( 1987 ) proved this for some elliptic curves of rank at most 1 with complex multiplication . …

WebJan 31, 2024 · Check the AMS fonts documentation; unless memory fails, it contains instructions for accessing the cyrillic font, specifically using \Sha as an example. ( texdoc amsfndoc) (But if this fails, send a message to MR asking for instructions. They surely use this notation.) @Davislor -- As of last summer, Math Reviews was nowhere near being … WebDec 21, 2024 · There is a related notion of the Shafarevich-Tate group associated to a Lagrangian fibration. Its connected component of unity can be shown to be isomorphic to …

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. … 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 …

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 …

WebThe object E being an elliptic curve over a number field, returns a real number c such that the BSD conjecture predicts that L E (r) (1)/r != c R S where r is the rank, R the regulator and S the cardinal of the Tate-Shafarevich group. raenomWebON TATE-SHAFAREVICH GROUPS OF ABELIAN VARIETIES CRISTIAN D. GONZALEZ-AVILES (Communicated by David E. Rohrlich) To Ricardo Baeza with gratitude Abstract. Let K=Fbe … raenobandzWebJan 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 … dr amitava royWebelliptic curves of high rank to Shafarevich-Tate groups of abelian varieties of rank 0, I found a construction of nonsquare Shafarevich-Tate groups. The Main Theorem Theorem … dr amitha gona salem oregonWebMar 6, 2024 · The Tate–Shafarevich conjecture states that the Tate–Shafarevich group is finite. Karl Rubin proved this for some elliptic curves of rank at most 1 with complex multiplication . [5] Victor A. Kolyvagin extended this to modular elliptic curves over the rationals of analytic rank at most 1 (The modularity theorem later showed that the … dr amitoj takharWebNéron models, Tamagawa factors, and Tate-Shafarevich groups Brian Conrad October 14, 2015 1 Motivation LetRbeadiscretevaluationring, F= Frac(R), andkitsresiduefield. Let Abe … dr amit nanavatiWebTate-Shafarevich group¶. 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 map to zero under … ra enjoy