The Selmer Group, the Shafarevich-tate Group, and the Weak Mordell-weil Theorem
نویسنده
چکیده
This is an introduction to classical descent theory, in the context of abelian varieties over number fields.
منابع مشابه
Ranks of Twists of Elliptic Curves and Hilbert’s Tenth Problem
In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) that have a given 2-Selmer rank. As a consequence, under appropriate hypotheses we can find m...
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