Vol. 14, No. 1, 2020

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Supersingular Hecke modules as Galois representations

Elmar Grosse-Klönne

Vol. 14 (2020), No. 1, 67–118
DOI: 10.2140/ant.2020.14.67
Abstract

Let F be a local field of mixed characteristic (0,p), let k be a finite extension of its residue field, let be the pro-p-Iwahori Hecke k-algebra attached to GLd+1(F) for some d 1. We construct an exact and fully faithful functor from the category of supersingular -modules to the category of Gal(F̄F)-representations over k. More generally, for a certain k-algebra surjecting onto we define the notion of -supersingular modules and construct an exact and fully faithful functor from the category of -supersingular -modules to the category of Gal(F̄F)-representations over k.

Keywords
pro-$p$ Iwahori Hecke algebra, supersingular module, Galois representation, $(\varphi, \Gamma)$-module
Mathematical Subject Classification 2010
Primary: 11F85
Milestones
Received: 10 December 2018
Revised: 6 May 2019
Accepted: 1 September 2019
Published: 15 March 2020
Authors
Elmar Grosse-Klönne
Mathematisch-Naturwissenschaftliche Fakultät, Institut für Mathematik
Humboldt-Universität zu Berlin
Germany