A Weil-étale version of the Birch and Swinnerton-Dyer formula over function fields

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The Birch and Swinnerton-Dyer conjectural formula Project description

This proposal falls broadly in the area of number theory and more specifically in arithmetic geometry. It is concerned with a part of the Birch and Swinnerton-Dyer (BSD) conjecture on elliptic curves and abelian varieties. A fundamental problem of number theory is: given a set of polynomial equations with rational coefficients, find all of its rational solutions and investigate their structure....

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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...

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ژورنال

عنوان ژورنال: Journal of Number Theory

سال: 2020

ISSN: 0022-314X

DOI: 10.1016/j.jnt.2019.08.013