Browsing by Author "Booher, Jeremy"

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    G-valued crystalline deformation rings in the Fontaine–Laffaille range
    (Cambridge University Press, 2023) Booher, Jeremy; Levin, Brandon; Mathematics
    Let G be a split reductive group over the ring of integers in a ppp-adic field with residue field FF\mathbf {F}. Fix a representation ¯ρρ¯¯¯\overline {\rho } of the absolute Galois group of an unramified extension of QpQp\mathbf {Q}_p, valued in G(F)G(F)G(\mathbf {F}). We study the crystalline deformation ring for ¯ρρ¯¯¯\overline {\rho } with a fixed ppp-adic Hodge type that satisfies an analog of the Fontaine–Laffaille condition for GGG-valued representations. In particular, we give a root theoretic condition on the ppp-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.