2018/02/28 by Jan Kohlhaase, Kohlhaase, Jan
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1802.10502
openalex publication_date 2018/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be the group of rational points of a split connected reductive group over a nonarchimedean local field of residue characteristic p. Let I be a pro-p Iwahori subgroup of G and let R be a commutative quasi-Frobenius ring. If H=R[I\backslash G/I] denotes the pro-p Iwahori-Hecke algebra of G over R we clarify the relation between the category of H-modules and the category of G-equivariant coefficient systems on the semisimple Bruhat-Tits building of G. If R is a field of characteristic zero this yields alternative proofs of the exactness of the Schneider-Stuhler resolution and of the Zelevinski conjecture for smooth G-representations generated by their I-invariants. In general, it gives a description of the derived category of H-modules in terms of smooth G-representations and yields a functor to generalized (φ,Γ)-modules extending the constructions of Colmez, Schneider and Vignéras.