Reductions of an elliptic curve and their Tate-Shafarevich groups

Author： Cojocaru A. C.  

Publisher： Springer Publishing Company

ISSN： 0025-5831

Source： Mathematische Annalen, Vol.329, Iss.3, 2004-07, pp. : 513-534

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Abstract

In this paper we study the Tate-Shafarevich groups III p of the reductions modulo primes p of an elliptic curve E/ considered as being defined over their function fields. Assuming GRH when E has no CM, we show that III p is trivial for a positive proportion of primes p, provided E has an irrational point of order two.

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