ON THE TATE-SHAFAREVICH GROUPS OVER BIQUADRATIC EXTENSIONS Yu, Hoseog;
Let A be an abelian variety defined over a number field K. Let L be a biquadratic extension of K with Galois group G and let III (A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and over L. Assuming III(A/L) is finite, we compute [III(A/K)]/[III(A/L)] where [X] is the order of a finite abelian group X.
Tate-Shafarevich group;abelian varieties;restriction of scalars;
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