The eigencurve at crystalline points with scalar Frobenius and Gross-Stark regulators

Adel  Betina; Aleksandre  Maksoud; Alice Pozzi

doi:10.48550/arXiv.2502.00876

The eigencurve at crystalline points with scalar Frobenius and Gross-Stark regulators

Adel Betina^*, Aleksandre Maksoud, Alice Pozzi

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

A complete description of the local geometry of the p-adic eigencurve at p-irregular classical weight one cusp forms is given in the cases where the usual R=T methods fall short. As an application, we show that the ordinary p-adic étale cohomology group attached to the tower of elliptic modular curves X1(Npr) is not free over the Hecke algebra, when localized at a p-irregular weight one point.

Original language	English
Pages (from-to)	169-228
Number of pages	60
Journal	Journal für die reine und angewandte Mathematik
Volume	2026
Issue number	834
Early online date	3 Apr 2026
DOIs	https://doi.org/10.48550/arXiv.2502.00876 https://doi.org/10.1515/crelle-2026-0023
Publication status	Published - 1 May 2026

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title = "The eigencurve at crystalline points with scalar Frobenius and Gross-Stark regulators",

abstract = "A complete description of the local geometry of the p-adic eigencurve at p-irregular classical weight one cusp forms is given in the cases where the usual R=T methods fall short. As an application, we show that the ordinary p-adic {\'e}tale cohomology group attached to the tower of elliptic modular curves X1(Npr) is not free over the Hecke algebra, when localized at a p-irregular weight one point.",

author = "Adel Betina and Aleksandre Maksoud and Alice Pozzi",

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doi = "10.48550/arXiv.2502.00876",

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T1 - The eigencurve at crystalline points with scalar Frobenius and Gross-Stark regulators

AU - Betina, Adel

AU - Maksoud, Aleksandre

AU - Pozzi, Alice

PY - 2026/5/1

Y1 - 2026/5/1

N2 - A complete description of the local geometry of the p-adic eigencurve at p-irregular classical weight one cusp forms is given in the cases where the usual R=T methods fall short. As an application, we show that the ordinary p-adic étale cohomology group attached to the tower of elliptic modular curves X1(Npr) is not free over the Hecke algebra, when localized at a p-irregular weight one point.

AB - A complete description of the local geometry of the p-adic eigencurve at p-irregular classical weight one cusp forms is given in the cases where the usual R=T methods fall short. As an application, we show that the ordinary p-adic étale cohomology group attached to the tower of elliptic modular curves X1(Npr) is not free over the Hecke algebra, when localized at a p-irregular weight one point.

U2 - 10.48550/arXiv.2502.00876

DO - 10.48550/arXiv.2502.00876

M3 - Article (Academic Journal)

SN - 0075-4102

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JO - Journal für die reine und angewandte Mathematik

JF - Journal für die reine und angewandte Mathematik

IS - 834

ER -

The eigencurve at crystalline points with scalar Frobenius and Gross-Stark regulators

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