WebNov 4, 2024 · Empirical analysis is often the first step towards the birth of a conjecture. This is the case of the Birch-Swinnerton-Dyer (BSD) Conjecture describing the rational points on an elliptic curve, one of the most celebrated unsolved problems in mathematics. Here we extend the original empirical approach, to the analysis of the Cremona database of … WebMar 15, 2024 · We study the finite abelian groups K(,2)(o), where o denotes the ring of integers of a totally real number field. As a major tool we employ the Birch-Tate conjecture which states that the order of K(,2)(o) can be computed via the Dedekind zeta-function. The odd part of this conjecture has been proved for abelian fields as a consequence of the …
Birch and Swinnerton-Dyer conjecture - Wikipedia
WebBirch, B. J., and N. M. Stephens:The parity of the rank of the Mordell-Weil group. Topology 5, 295–299 (1966). CrossRef MathSciNet MATH Google Scholar ... Lang, S.: Les formes bilinéaires de Néron et Tate. Sém. Bourbaki 274 (1964). Google Scholar Mordell, L. J. : On the rational solution of the indeterminate equations of the third and ... WebLichtenbaum then made a general conjecture combining the Birch-Tate conjec-tureandBorel. That story was for number fields. Number fields are very special; for instance, there’s basically no other class of fields for which we know finite generation of the K-theory. Bloch conjectured a relation between L(E;2) (for E an elliptic curve over a green and white motorcycle helmet
Contents The Birch{Swinnerton-Dyer conjecture
WebIn mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve.It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after … WebSo the Tate conjecture would make much of algebraic geometry and number theory accessible to computation. More broadly, the Tate conjecture is closely intertwined with several of the other central conjectures of number theory and algebraic geometry, including the Hodge conjecture and the Birch{Swinnerton-Dyer conjecture. Even if the Tate … WebNov 20, 2024 · A Relation Between the 2-Primary Parts of the Main Conjecture and the Birch-Tate-Conjecture - Volume 32 Issue 2 Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a … flowers and wine gift sets