PreprintarXiv licencearXiv
Fine structure of even Galois deformation rings
Abstract
For every even Galois representation in a family of prime conductor ℓ, we prove that if k ∈ ℤ≥ 1 is maximal such that ℓ ≡ 1 bmod 3k then the even mod $3$ deformation ring RS ⊗ℤ3 𝔽3 of level S={ℓ,3} does not have a quotient isomorphic to 𝔽3[T]/(T2+3k−1). As a corollary, we deduce that the global even deformation rings RS are finite and flat in the category of ℤ3-modules.
Related
- Galois deformation rings and modularity in the residually reducible case
- On the dimension conjecture for global Galois deformation rings in characteristic two
- Galois-modular obstructions to the categorification of near-group fusion rings
- Bivariate Affine q-Krawtchouk Polynomials and Association Schemes over Galois Rings
- Finite Matrix Rings of Even Size Are Determined by Their Commuting Graphs
BibTeX
@misc{uttenthal2026fine,
title = {{Fine structure of even Galois deformation rings}},
author = {Peter Vang Uttenthal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17865},
eprint = {2610.17865},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17865},
}
RIS
TY - UNPB
TI - Fine structure of even Galois deformation rings
AU - Peter Vang Uttenthal
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17865
UR - https://arxiv.org/abs/2610.17865
AB - For every even Galois representation in a family of prime conductor ℓ, we prove that if k ∈ ℤ_≥ 1 is maximal such that ℓ ≡ 1 bmod 3^k then the even mod $3$ deformation ring R_S ⊗_ℤ_3 𝔽_3 of level S={ℓ,3} does not have a quotient isomorphic to 𝔽_3[T]/(T^2+3^k−1). As a corollary, we deduce that the global even deformation rings R_S are finite and flat in the category of ℤ_3-modules.
ER -