Extensions for supersingular representations of GL₂(Q_p)

2007/10/04 by Paskunas, Vytautas · 2 citations
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0710.1053

Abstract

Let p>2 be a prime number. Let G:=GL₂(Q_p) and π, τ smooth irreducible representations of G on F_p-vector spaces with a central character. We show if π is supersingular then Ext¹_G(τ,π)≠ 0 implies τ≅ π. This answers affirmatively for p>2 a question of Colmez. We also determine Ext¹_G(τ,π), when π is the Steinberg representation. As a consequence of our results combined with those already in the literature one knows Ext¹_G(τ,π) for all irreducible representations of G.

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