AN IRREDUCIBILITY CRITERION FOR SUPERSINGULAR mod p REPRESENTATIONS OF GL2(F ) FOR TOTALLY RAMIFIED EXTENSIONS F OF Qp

ON THE UNIVERSAL SUPERSINGULAR MOD p REPRESENTATIONS OF GL 2 ( F )

The irreducible supersingular mod p representations of G = GL2(F ), where F is a finite extension of Qp, are the building blocks of the mod p representation theory of G. They all arise as irreducible quotients of certain universal supersingular representations. We investigate the structure of these universal modules in the case when F/Qp is totally ramified.

Extensions for supersingular representations of GL2(Qp)

On F - Crystalline Representations

We extend the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. In particular, for a finite and totally ramified extension F/Qp, and an arbitrary finite extension K/F , we construct a general class of infinite and totally wildly ramified extensions K∞/K so that the functor V 7→ V |GK∞ is fully-faithfull on the category of F ...

THE CLASSIFICATION OF IRREDUCIBLE ADMISSIBLE MOD p REPRESENTATIONS OF A p-ADIC GLn

Let F be a finite extension of Qp. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F -split p-adic reductive group over Fp to be supersingular. We then give the classification of irreducible admissible smooth GLn(F )-representations over Fp in terms of supersingular representations. As a consequence we deduce that supersingular...

A SATAKE ISOMORPHISM IN CHARACTERISTIC p

Suppose that G is a connected reductive group over a p-adic field F , that K is a hyperspecial maximal compact subgroup of G(F ), and that V is an irreducible representation of K over the algebraic closure of the residue field of F . We establish an analogue of the Satake isomorphism for the Hecke algebra of compactly supported, Kbiequivariant functions f : G(F ) EndV . These Hecke algebras wer...