Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.12830 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this paper, we apply the Taylor--Wiles--Kisin patching method to the coherent cohomology of modular curves at minimal level. We establish a multiplicity-one result for the patched module by the $q$-expansion principle and show that a certain partial normalization of the crystalline deformation ring is Cohen--Macaulay. As applications, we prove new cases where crystalline deformation rings are Cohen--Macaulay, establish a Zariski density result for crystalline points in characteristic $p$, and prove a multiplicity-one result for Serre's mod-$p$ quaternionic modular forms.