On Tate-Shafarevich groups of abelian varieties |
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Authors: | Cristian D Gonzalez-Avilé s |
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Institution: | Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile |
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Abstract: | Let be a finite Galois extension of number fields with Galois group , let be an abelian variety defined over , and let and denote, respectively, the Tate-Shafarevich groups of over and of over . Assuming that these groups are finite, we derive, under certain restrictions on and , a formula for the order of the subgroup of of -invariant elements. As a corollary, we obtain a simple formula relating the orders of , and when is a quadratic extension and is the twist of by the non-trivial character of . |
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Keywords: | |
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