Stability in the category of smooth mod-p representations of SL₂(Qp)

2023/04/05 by Konstantin Ardakov, Peter Schneider, Ardakov, Konstantin +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2304.02585

openalex publication_date 2023/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p ≥ 5 be a prime number and let G = SL₂(ℚ_p). Let Ξ = Spec(Z) denote the spectrum of the centre Z of the pro-p Iwahori Hecke algebra of G with coefficients in a field k of characteristic p. Let R ⊂ Ξ× Ξ denote the support of the pro-p Iwahori Ext-algebra of G, viewed as a (Z,Z)-bimodule. We show that the locally ringed space Ξ/R is a projective algebraic curve over Spec(k) with two connected components, and that each connected component is a chain of projective lines. For each Zariski open subset U of Ξ/R, we construct a stable localising subcategory L_U of the category of smooth k-linear representations of G.

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