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Vanishing of Sha(A/K)[P∞] and its consequences for the anticyclotomic Iwasawa theory of GL2-abelian varieties

  • Luca Mastella
  • Ahmed Matar
  • Francesco Zerman
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Abstract

In this article we generalise a classical Kolyvagin's result on the vanishing of the p-part of the Shafarevich--Tate group of an elliptic curve (defined over ℚ) over an imaginary quadratic field K to modular abelian varieties of GL2-type (defined over a totally real number field F) and a CM field K/F. Combining this result with the abstract Iwasawa-theoretical argument of [MN19], we show that a similar vanishing holds over the layers of a suitably defined anticyclotomic multi-ℤp-extension of K.

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Cite

BibTeXRIS
BibTeX
@misc{mastella2026vanishing,
  title = {{Vanishing of $\mathrmSha(A/K)[\mathfrakP^\infty]$ and its consequences for the anticyclotomic Iwasawa theory of $\mathrmGL_2$-abelian varieties}},
  author = {Luca Mastella and Ahmed Matar and Francesco Zerman},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29337},
  eprint = {2608.29337},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29337},
}
RIS
TY  - UNPB
TI  - Vanishing of Sha(A/K)[P^∞] and its consequences for the anticyclotomic Iwasawa theory of GL_2-abelian varieties
AU  - Luca Mastella
AU  - Ahmed Matar
AU  - Francesco Zerman
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29337
UR  - https://arxiv.org/abs/2608.29337
AB  - In this article we generalise a classical Kolyvagin's result on the vanishing of the p-part of the Shafarevich--Tate group of an elliptic curve (defined over ℚ) over an imaginary quadratic field K to modular abelian varieties of GL_2-type (defined over a totally real number field F) and a CM field K/F. Combining this result with the abstract Iwasawa-theoretical argument of [MN19], we show that a similar vanishing holds over the layers of a suitably defined anticyclotomic multi-ℤ_p-extension of K.
ER  -