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On Density of Modular Points in Pseudo-Deformation Rings

Deo, SV (2023) On Density of Modular Points in Pseudo-Deformation Rings. In: International Mathematics Research Notices, 2023 (21). pp. 18443-18499.

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Official URL: https://doi.org/10.1093/imrn/rnad037


Given a continuous, odd, reducible, and semi-simple 2-dimensional representation ��0 of GQ,Np over a finite field of odd characteristic p, we study the relation between the universal deformation ring of the pseudo-representation corresponding to ��0 (pseudo-deformation ring) and the big p-adic Hecke algebra to prove that the maximal reduced quotient of the pseudo-deformation ring is isomorphic to the local component of the big p-adic Hecke algebra corresponding to ��0 if a certain global Galois cohomology group has dimension 1. This partially extends the results of Böckle to the case of residually reducible representations. We give an application of our main theorem to the structure of Hecke algebras modulo p. As another application of our methods and results, we prove a result about non-optimal levels of newforms lifting ��0 in the spirit of Diamond�Taylor. This also gives a partial answer to a conjecture of Billerey�Menares. © 2023 Oxford University Press. All rights reserved.

Item Type: Journal Article
Publication: International Mathematics Research Notices
Publisher: Oxford University Press
Additional Information: The copyright for this article belongs to author.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 29 Feb 2024 06:22
Last Modified: 29 Feb 2024 06:22
URI: https://eprints.iisc.ac.in/id/eprint/83745

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