Generic smoothness for G-valued potentially semi-stable deformation rings

Bellovin, R. (2016) Generic smoothness for G-valued potentially semi-stable deformation rings. Annales de l'Institut Fourier, 66(6), pp. 2565-2620. (doi: 10.5802/aif.3072)

Abstract

We extend Kisin’s results on the structure of characteristic 0 Galois deformation rings to deformation rings of Galois representations valued in arbitrary connected reductive groups G. In particular, we show that such Galois deformation rings are complete intersections. In addition, we study explicitly the structure of the moduli space Xϕ,N of (framed) (ϕ, N)-modules when G = GLn. We show that when G = GL3 and K0 = Qp, Xϕ,N has a singular irreducible component, and we construct a moduli-theoretic resolution of singularities.

• Item Type: Articles
• Additional Information: This work was partially supported by an NSF Graduate Research Fellowship.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bellovin, Dr Rebecca
• Authors: Bellovin, R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Annales de l'Institut Fourier
• Publisher: Association des Annales de l'Institut Fourier
• ISSN: 0373-0956
• ISSN (Online): 1777-5310
• Published Online: 04 October 2016
• Copyright Holders: Copyright © 2016 Association des Annales de l’institut Fourier, Certains droits réservés
• First Published: First published in Annales de l'Institut Fourier 66(6):2565-2620
• Publisher Policy: Reproduced under a Creative Commons license