G-valued crystalline deformation rings in the Fontaine–Laffaille range

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dc.citation.firstpage1791
dc.citation.issueNumber8
dc.citation.journalTitleCompositio Mathematica
dc.citation.lastpage1832
dc.citation.volumeNumber159
dc.contributor.authorBooher, Jeremy
dc.contributor.authorLevin, Brandon
dc.date.accessioned2024-05-03T15:51:10Z
dc.date.available2024-05-03T15:51:10Z
dc.date.issued2023
dc.description.abstractLet 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.
dc.identifier.citationBooher, J., & Levin, B. (2023). G-valued crystalline deformation rings in the Fontaine–Laffaille range. Compositio Mathematica, 159(8), 1791–1832. https://doi.org/10.1112/S0010437X23007297
dc.identifier.digitalg-valued-crystalline-deformation
dc.identifier.doihttps://doi.org/10.1112/S0010437X23007297
dc.identifier.urihttps://hdl.handle.net/1911/115552
dc.language.isoeng
dc.publisherCambridge University Press
dc.rightsExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license. Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleG-valued crystalline deformation rings in the Fontaine–Laffaille range
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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