On the Birch and Swinnerton-Dyer conjecture for abelian varieties attached to Hilbert modular forms
نویسندگان
چکیده
منابع مشابه
A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties
Mazur, Tate, and Teitelbaum gave a p-adic analogue of the Birch and Swinnerton-Dyer conjecture for elliptic curves. We provide a generalization of their conjecture in the good ordinary case to higher dimensional modular abelian varieties over the rationals by constructing the padic L-function of a modular abelian variety and showing it satisfies the appropriate interpolation property. We descri...
متن کاملThe Birch-swinnerton-dyer Conjecture
We give a brief description of the Birch-Swinnerton-Dyer conjecture which is one of the seven Clay problems.
متن کاملThe Birch and Swinnerton-Dyer Conjecture for Abelian Varieties over Number Fields
1 Algebraic Groups 7 1.1 Group Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Restriction of Scalars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Algebraic Groups over a Nonalgebraically Closed Field K . . . . . . . . . . . 13 1.4 Structure of Algebraic Groups . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Topologizing G(R...
متن کاملVisible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero
This paper provides evidence for the Birch and Swinnerton-Dyer conjecture for analytic rank 0 abelian varieties Af that are optimal quotients of J0(N) attached to newforms. We prove theorems about the ratio L(Af , 1)/ΩAf , develop tools for computing with Af , and gather data about certain arithmetic invariants of the nearly 20, 000 abelian varieties Af of level ≤ 2333. Over half of these Af ha...
متن کاملThe Birch and Swinnerton-Dyer Conjecture
A polynomial relation f(x, y) = 0 in two variables defines a curve C. If the coefficients of the polynomial are rational numbers then one can ask for solutions of the equation f(x, y) = 0 with x, y ∈ Q, in other words for rational points on the curve. If we consider a non-singular projective model C of the curve then over C it is classified by its genus. Mordell conjectured, and in 1983 Falting...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2011
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2010.11.008