ON THE IRREDUCIBLE COMPONENTS OF SOME CRYSTALLINE DEFORMATION RINGS
Forum of Mathematics, Sigma, Tome 8 (2020)
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We adapt a technique of Kisin to construct and study crystalline deformation rings of $G_{K}$ for a finite extension $K/\mathbb{Q}_{p}$. This is done by considering a moduli space of Breuil–Kisin modules, satisfying an additional Galois condition, over the unrestricted deformation ring. For $K$ unramified over $\mathbb{Q}_{p}$ and Hodge–Tate weights in $[0,p]$, we study the geometry of this space. As a consequence, we prove that, under a mild cyclotomic-freeness assumption, all crystalline representations of an unramified extension of $\mathbb{Q}_{p}$, with Hodge–Tate weights in $[0,p]$, are potentially diagonalizable.
@article{10_1017_fms_2020_12,
author = {ROBIN BARTLETT},
title = {ON {THE} {IRREDUCIBLE} {COMPONENTS} {OF} {SOME} {CRYSTALLINE} {DEFORMATION} {RINGS}},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {8},
year = {2020},
doi = {10.1017/fms.2020.12},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.12/}
}
ROBIN BARTLETT. ON THE IRREDUCIBLE COMPONENTS OF SOME CRYSTALLINE DEFORMATION RINGS. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.12
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