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

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dc.citation.firstpage1791en_US
dc.citation.issueNumber8en_US
dc.citation.journalTitleCompositio Mathematicaen_US
dc.citation.lastpage1832en_US
dc.citation.volumeNumber159en_US
dc.contributor.authorBooher, Jeremyen_US
dc.contributor.authorLevin, Brandonen_US
dc.contributor.orgMathematicsen_US
dc.date.accessioned2024-05-03T15:51:10Zen_US
dc.date.available2024-05-03T15:51:10Zen_US
dc.date.issued2023en_US
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.en_US
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/S0010437X23007297en_US
dc.identifier.digitalg-valued-crystalline-deformationen_US
dc.identifier.doihttps://doi.org/10.1112/S0010437X23007297en_US
dc.identifier.urihttps://hdl.handle.net/1911/115552en_US
dc.language.isoengen_US
dc.publisherCambridge University Pressen_US
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.en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.titleG-valued crystalline deformation rings in the Fontaine–Laffaille rangeen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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