Duke Mathematical Journal
- Duke Math. J.
- Volume 165, Number 8 (2016), 1529-1595.
From pro- Iwahori–Hecke modules to -modules, I
Let be the ring of integers in a finite extension of , and let be its residue field. Let be a split reductive group over , and let be a maximal split torus in . Let be the pro- Iwahori–Hecke -algebra. Given a semi-infinite reduced chamber gallery (alcove walk) in the -stable apartment, a period of of length , and a homomorphism compatible with , we construct a functor from the category of finite-length -modules to étale -modules over Fontaine’s ring . If , then there are essentially two choices of with , both leading to a functor from to étale -modules and hence to -representations. Both induce a bijection between the set of absolutely simple supersingular -modules of dimension and the set of irreducible representations of over of dimension . We also compute these functors on modular reductions of tamely ramified locally unitary principal series representations of over . For , we recover Colmez’s functor (when restricted to -torsion -representations generated by their pro- Iwahori invariants).
Duke Math. J., Volume 165, Number 8 (2016), 1529-1595.
Received: 14 February 2014
Revised: 17 July 2015
First available in Project Euclid: 25 February 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F85: $p$-adic theory, local fields [See also 14G20, 22E50]
Secondary: 11F80: Galois representations 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Grosse-Klönne, Elmar. From pro- $p$ Iwahori–Hecke modules to $(\varphi,\Gamma)$ -modules, I. Duke Math. J. 165 (2016), no. 8, 1529--1595. doi:10.1215/00127094-3450101. https://projecteuclid.org/euclid.dmj/1456412785