In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to...

Birch FRS (born 25 September 1931) is a British mathematician. His name has been given to the Birch and Swinnerton-Dyer conjecture. Bryan John Birch was...

group of rational points of the elliptic curve over K by the Birch and Swinnerton-Dyer conjecture. The description of the Hasse–Weil zeta function up to finitely...

As a mathematician he was best known for his part in the Birch and Swinnerton-Dyer conjecture relating algebraic properties of elliptic curves to special...

unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem,...

Birch and Swinnerton-Dyer conjecture (BSD) is one of the Millennium problems of the Clay Mathematics Institute. The conjecture relies on analytic and...

more general L-functions and as a still-open research problem, is the conjecture developed by Bryan Birch and Peter Swinnerton-Dyer in the early part of the...

remarkable properties that appear in the statement of the Birch and Swinnerton-Dyer conjecture. Reduction of an abelian variety A modulo a prime ideal of...

and used this to prove much of the Birch–Swinnerton-Dyer conjecture for rank 1 elliptic curves. Brown proved the Birch–Swinnerton-Dyer conjecture for...

Q$ satisfy the Birch and Swinnerton-Dyer conjecture", arXiv:1407.1826 [math.NT] Coates, John; Sujatha, R. (2006), Cyclotomic Fields and Zeta Values, Springer...

In the mathematical field of geometric topology, the Poincaré conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about...

Birch and Swinnerton-Dyer conjecture Hodge conjecture Navier–Stokes existence and smoothness P versus NP Riemann hypothesis Yang–Mills existence and mass...

Peter Swinnerton-Dyer, English mathematician Milborne-Swinnerton-Pilkington Baronets, title in the Baronetage of Nova Scotia Birch and Swinnerton-Dyer conjecture...

Game complexity List of unsolved problems in mathematics Unique games conjecture Unsolved problems in computer science A nondeterministic Turing machine...

Bad reduction See good reduction. Birch and Swinnerton-Dyer conjecture The Birch and Swinnerton-Dyer conjecture on elliptic curves postulates a connection...

Thus modulo squares any integer can be the order of Ш. Birch and Swinnerton-Dyer conjecture Lang & Tate 1958. Shafarevich 1959. Cassels 1962b. Cassels...

In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular...

hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

multiple zeros at the real point of their critical line; the Birch-Swinnerton-Dyer conjecture predicts that the multiplicity of this zero is the rank of...

mathematics. The first conjecture, which is known as the "smoothness" conjecture, states that there should always exist smooth and globally defined solutions...

smooth over k(C). Then the Tate conjecture for divisors on X is equivalent to the Birch and Swinnerton-Dyer conjecture for the Jacobian variety of F. By...

principle. Despite its great importance, for example in the Birch and Swinnerton-Dyer conjecture, it proved very difficult to get any control of it, until...

partial resolution to the congruent number problem, and under the Birch and Swinnerton-Dyer conjecture, a full resolution. The congruent number problem asks...

Ramanujan–Petersson conjecture Birch and Swinnerton-Dyer conjecture Automorphic form Selberg trace formula Artin conjecture Sato–Tate conjecture Langlands program...

called the Tamagawa number conjecture, a name arising via the Birch–Swinnerton-Dyer conjecture and its formulation as an elliptic curve analogue of the Tamagawa...

computational problem, and does not always have effective solutions. Meaning of the rank: see Birch and Swinnerton-Dyer conjecture. Possible torsion subgroups:...

existence and smoothness The Birch and Swinnerton-Dyer conjecture Some of the mathematicians who were involved in the selection and presentation of the seven...

$\mathbb Q$ satisfy the Birch and Swinnerton-Dyer conjecture". arXiv:1407.1826 [math.NT]. Baker, Matt (10 March 2014). "The BSD conjecture is true for most elliptic...

1007/bf02418270 Schupp & Lyndon 2001 La Harpe 2000 See the Birch and Swinnerton-Dyer conjecture, one of the millennium problems Abramovich, Dan; Karu, Kalle;...