On the universal mod p supersingular quotients for GL2(F) over F‾p for a general F/Qp

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Abstract

Let F/Qp be a finite extension. We explore the universal supersingular mod p representations of GL2(F) by computing a basis for their spaces of invariants under the pro-p Iwahori subgroup. This generalizes works of Breuil and Schein (from Qp and the totally ramified cases to an arbitrary extension F/Qp). Using these results we then construct, for an unramified F/Qp, quotients of the universal supersingular modules which have as quotients all the supersingular representations of GL2(F) with a GL2(OF)-socle that is expected to appear in the mod p local Langlands correspondence. A construction in the case of an extension of Qp with inertia degree 2 and suitable ramification index is also presented.

Original languageEnglish (US)
Pages (from-to)1-38
Number of pages38
JournalJournal of Algebra
Volume519
DOIs
StatePublished - Feb 1 2019

Keywords

  • Galois representations
  • Supersingular representations
  • Weight part of Serre's conjecture
  • mod p local Langlands correspondence

ASJC Scopus subject areas

  • Algebra and Number Theory

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