Computations About Tate-Shafarevich Groups Using Iwasawa Theory

Abstract

We explain how to combine deep results from Iwasawa theory with explicit computation to obtain information about p-parts of Tate-Shafarevich groups of elliptic curves over Q. This method provides a practical way to compute #X(E/Q)(p) in many cases when traditional p-descent methods are completely impractical and also in situations where results of Kolyvagin… (More)

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