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Variation of Shafarevich-Tate groups in Hida families
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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BibTeX
@misc{ronche2026variation,
title = {{Variation of Shafarevich-Tate groups in Hida families}},
author = {Enrico Da Ronche and Matteo Longo and Stefano Vigni and Francesco Zerman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22226},
eprint = {2610.22226},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22226},
}
RIS
TY - UNPB
TI - Variation of Shafarevich-Tate groups in Hida families
AU - Enrico Da Ronche
AU - Matteo Longo
AU - Stefano Vigni
AU - Francesco Zerman
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22226
UR - https://arxiv.org/abs/2610.22226
AB - 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.
ER -