Vol. 9, No. 8, 2015

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11
Issue 4, 767–1007
Issue 3, 505–765
Issue 2, 253–503
Issue 1, 1–252

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
$G$-valued crystalline representations with minuscule $p$-adic Hodge type

Brandon Levin

Vol. 9 (2015), No. 8, 1741–1792
DOI: 10.2140/ant.2015.9.17

We study G-valued semistable Galois deformation rings, where G is a reductive group. We develop a theory of Kisin modules with G-structure and use this to identify the connected components of crystalline deformation rings of minuscule p-adic Hodge type with the connected components of moduli of “finite flat models with G-structure”. The main ingredients are a construction in integral p-adic Hodge theory using Liu’s theory of (φ,Ĝ)-modules and the local models constructed by Pappas and Zhu.

Galois representation, $p$-adic Hodge theory, finite flat group scheme, local model
Mathematical Subject Classification 2010
Primary: 11S20
Secondary: 14L15, 14F30
Received: 4 April 2014
Revised: 1 June 2015
Accepted: 15 July 2015
Published: 29 October 2015
Brandon Levin
Department of Mathematics
University of Chicago
5734 S. University Avenue, Room 208C
Chicago, 60637
United States