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PreprintCC BY 4.0arXiv

Refined conjectures on Fitting ideals of BDP Selmer groups

  • Chan-Ho Kim
  • Aprameyo Pal
  • Jishnu Ray
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Abstract

Under mild assumptions, we prove the strong main conjecture for BDP Selmer groups of elliptic curves with good reduction in the sense of Kurihara's refined Iwasawa theory. In particular, the structure of the initial Fitting ideal of BDP Selmer groups over finite subextensions in the anticyclotomic ℤp-extension is determined by the values of the corresponding p-adic modular form at CM points.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026refined,
  title = {{Refined conjectures on Fitting ideals of BDP Selmer groups}},
  author = {Chan-Ho Kim and Aprameyo Pal and Jishnu Ray},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17003},
  eprint = {2609.17003},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17003},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Refined conjectures on Fitting ideals of BDP Selmer groups
AU  - Chan-Ho Kim
AU  - Aprameyo Pal
AU  - Jishnu Ray
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17003
UR  - https://arxiv.org/abs/2609.17003
AB  - Under mild assumptions, we prove the strong main conjecture for BDP Selmer groups of elliptic curves with good reduction in the sense of Kurihara's refined Iwasawa theory. In particular, the structure of the initial Fitting ideal of BDP Selmer groups over finite subextensions in the anticyclotomic ℤ_p-extension is determined by the values of the corresponding p-adic modular form at CM points.
ER  -