Tate shafarevich group
WebAcademia.edu is a platform for academics to share research papers. Webis now known to be equivalent to the finiteness of the Tate–Shafarevich group, [20], [17, Corollary 9.7]. 4. A proof of the conjecture in the stronger form would give an effective means of finding generators for the group of rational points. Actually, one only needs the integrality of the term X C in the expression for L∗(C,s) above ...
Tate shafarevich group
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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.
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. 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 …
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 … WebAs 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 …
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WebMaster's Thesis : “The machine learning of the Class Group, the Tate-Shafarevich Group and the Rank of Elliptic Curves : towards a theory of artificial intelligence for mathematical research". Supervisor : Maryna Viazovska and Vlad Serban. McGill University Bachelor of Science (B.Sc.) Honours Mathematics. 2016 - ... ingersoll rand cameron pump divisionWebthe 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). ingersoll rand canada locationsWebSep 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 … ingersoll rand canada phone numberWebVISIBILITY 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. mitotic figures cytologyWebTate-Shafarevich groups over finitely generated fields. 6. Relationship between Tate-Shafarevich group and the BSD conjecture. 3. Is the Tate-Shafarevich group of a rational … mitotic g1-g1/s phasesWebJan 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 … ingersoll rand buys traneWebApr 12, 2003 · In this paper it is shown that for every prime p>5 the dimension of the p-torsion in the Tate-Shafarevich group of E/K can be arbitrarily large, where E is an elliptic curve defined over a number ... ingersoll rand cbv