Year: 2026
Type: preprint
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 $\mathbf{f}$.
Source: arXiv (Cornell University)
Institutions: UniDistance Suisse, University of Genoa
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5622661325
OpenAlex ID: W7222403678