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- Title
G -valued crystalline deformation rings in the Fontaine–Laffaille range.
- Authors
Booher, Jeremy; Levin, Brandon
- Abstract
Let $G$ be a split reductive group over the ring of integers in a $p$ -adic field with residue field $\mathbf {F}$. Fix a representation $\overline {\rho }$ of the absolute Galois group of an unramified extension of $\mathbf {Q}_p$ , valued in $G(\mathbf {F})$. We study the crystalline deformation ring for $\overline {\rho }$ with a fixed $p$ -adic Hodge type that satisfies an analog of the Fontaine–Laffaille condition for $G$ -valued representations. In particular, we give a root theoretic condition on the $p$ -adic Hodge type which ensures that the crystalline deformation ring is formally smooth. Our result improves on all known results for classical groups not of type A and provides the first such results for exceptional groups.
- Subjects
RINGS of integers; GROUP extensions (Mathematics); GROUP rings; HODGE theory
- Publication
Compositio Mathematica, 2023, Vol 159, Issue 8, p1791
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X23007297