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arXiv · 2610.22226

Variation of Shafarevich-Tate groups in Hida families

Enrico Da Ronche·Matteo Longo·Stefano Vigni·Francesco Zerman
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Abstract

Let $\mathbf{f}$ 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 $\mathbf{f}$ 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 $\mathbf{f}$.

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Enrico Da Ronche, Matteo Longo, Stefano Vigni, Francesco Zerman. 2026-10-15. Variation of Shafarevich-Tate groups in Hida families. https://arxiv.org/abs/2610.22226

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