PreprintCC BY 4.0arXiv
On Hecke algebras at exceptional Eisenstein primes
Abstract
We study the structure over ℤp of the Hecke algebra acting on ordinary cusp forms in the Eisenstein, non-p-distinguished case. Our results and methods draw on four complementary approaches: deformation theory, through R=T theorems; Iwasawa theory, through connections to Sharifi's conjecture; p-adic L-functions, through an exceptional zero formula; and computational experiments using Magma. We also obtain new results regarding the Coleman--Greenberg conjecture.
Related
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BibTeX
@misc{maksoud2026hecke,
title = {{On Hecke algebras at exceptional Eisenstein primes}},
author = {Alexandre Maksoud},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35559},
eprint = {2610.35559},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35559},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Hecke algebras at exceptional Eisenstein primes
AU - Alexandre Maksoud
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35559
UR - https://arxiv.org/abs/2610.35559
AB - We study the structure over ℤ_p of the Hecke algebra acting on ordinary cusp forms in the Eisenstein, non-p-distinguished case. Our results and methods draw on four complementary approaches: deformation theory, through R=T theorems; Iwasawa theory, through connections to Sharifi's conjecture; p-adic L-functions, through an exceptional zero formula; and computational experiments using Magma. We also obtain new results regarding the Coleman--Greenberg conjecture.
ER -