The Period-index Problem in Wc-groups Ii: Abelian Varieties
نویسنده
چکیده
We study the relationship between the period and the index of a principal homogeneous space over an abelian variety, obtaining results which generalize work of Cassels and Lichtenbaum on curves of genus one. In addition, we show that the p-torsion in the Shafarevich-Tate group of a fixed abelian variety over a number field k grows arbitarily large when considered over field extensions l/k of bounded degree. Essential use is made of an abelian variety version of O’Neil’s period-index obstruction.
منابع مشابه
The period-index problem in WC-groups IV: a local transition theorem
Let K be a complete discretely valued field with perfect residue field k. Assuming upper bounds on the relation between period and index for WC-groups over k, we deduce corresponding upper bounds on the relation between period and index for WC-groups over K. Up to a constant depending only on the dimension of the torsor, we recover theorems of Lichtenbaum and Milne in a “duality free” context. ...
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