A Mordell-weil Theorem for Abelian Varieties over Fields Generated by Torsion Points
نویسنده
چکیده
Let A be an abelian variety over a number field, Tl the ladic Tate module, and Gl the image of the Galois action on Tl. Then Hi(Gl, Tl) is a finite l-group which vanishes for l ≫ 0. We apply this bound for i = 1 and i = 2 to show that ifK denotes the field generated by all torsion points of A, then A(K) is the direct sum of its torsion group and a free abelian group.
منابع مشابه
18.782 Arithmetic Geometry Lecture Note 25
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تاریخ انتشار 2005