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ON THE TATE-SHAFAREVICH GROUPS OVER BIQUADRATIC EXTENSIONS
2015
Honam Mathematical Journal
Preserved Fulltext
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 X(A/K) and X(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and over L. Assuming X(A/L) is finite, we compute [X(A/K)]/[X(A/L)] where [X] is the order of a finite abelian group X.
doi:10.5831/hmj.2015.37.1.1
fatcat:jfojavfzazf7da4bw7wrjfjnhu