Variation of Shafarevich-Tate groups in Hida families
Enrico Da Ronche, Matteo Longo, Stefano Vigni, Francesco Zerman
Abstract
Let f be a Hida family of cusp forms over a standard (power series) Iwasawa algebra. We determine the pseudo-isomorphism class of the big Shafarevich-Tate group attached to f over a suitable imaginary quadratic field by describing all its higher Fitting ideals; this description is given in terms of the universal Kolyvagin system of Howard's big Heegner points. As a second contribution, we study the variation of the structure of the Shafarevich-Tate groups of the classical specializations of f.
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