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Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings

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Title: Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings
Authors: Wang Erickson, C
Item Type: Journal Article
Abstract: We construct and study the moduli of continuous representations of a profinite group with integral p-adic coefficients. We present this moduli space over the moduli space of continuous pseudorepresentations and show that this morphism is algebraizable. When this profinite group is the absolute Galois group of a p-adic local field, we show that these moduli spaces admit Zariski-closed loci cutting out Galois representations that are potentially semi-stable with bounded Hodge-Tate weights and a given Hodge and Galois type. As a consequence, we show that these loci descend to the universal deformation ring of the corresponding pseudorepresentation.
Editors: Gee, T
Issue Date: 24-Aug-2018
Date of Acceptance: 27-Aug-2016
URI: http://hdl.handle.net/10044/1/43809
DOI: https://dx.doi.org/10.1007/s00208-017-1557-8
ISSN: 1432-1807
Publisher: Springer Verlag (Germany)
Start Page: 1615
End Page: 1681
Journal / Book Title: Mathematische Annalen
Volume: 371
Issue: 3-4
Copyright Statement: © The Author(s) 2017 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: math.NT
math.AG
11F80 (Primary) 11S20, 14D15, 14L24 (Secondary)
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Online Publication Date: 2017-07-24
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences
Mathematics