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

  • Yu, Hoseog (Department of Mathematics, Sejong University)
  • Received : 2015.12.04
  • Accepted : 2016.01.25
  • Published : 2016.03.25

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($A_{\varphi}/K$)]/[III(A/L)], where [X] is the order of a finite abelian group X.

Keywords

Tate-Shafarevich group;abelian varieties;restriction of scalars

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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