ON THE TATE-SHAFAREVICH GROUPS OVER DEGREE 3 NON-GALOIS EXTENSIONS

• Journal title : Honam Mathematical Journal
• Volume 38, Issue 1,  2016, pp.85-93
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2016.38.1.85
Title & Authors
ON THE TATE-SHAFAREVICH GROUPS OVER DEGREE 3 NON-GALOIS EXTENSIONS
Yu, Hoseog;

Abstract
Let A be an abelian variety defined over a number field K and let L be a degree 3 non-Galois extension of K. Let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and over L. Assuming that III(A/L) is finite, we compute [III(A/K)][III($\small{A_{\varphi}/K}$)]/[III(A/L)], where [X] is the order of a finite abelian group X.
Keywords
Tate-Shafarevich group;abelian varieties;restriction of scalars;
Language
English
Cited by
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