2011/05/15 by Rachel Ollivier, Vincent Sécherre, Ollivier, Rachel +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1105.2957
arxiv created 2011/05/15 · openalex publication_date 2011/05/15 · arxiv updated 2011/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be a p-adic field with residue class field k. We investigate the structure of certain mod p universal modules for GL(3,F) over the corresponding Hecke algebras. To this end, we first study the structure of some mod p universal modules for the finite group GL(n,k) as modules over the corresponding Hecke algebras. We then relate this finite case to the p-adic one by using homological coefficient systems on the the affine Bruhat-Tits building of GL(3). Suppose now that k has cardinality p. We prove that the mod p universal module of GL(3,F) relative to the Iwahori subroup is flat and projective over the Iwahori-Hecke algebra. When replacing the Iwahori subgroup of GL(3,F) by its pro-p-radical, we prove that the corresponding module is flat over the pro-p Iwahori-Hecke algebra if and only if p=2.