2024/05/02 by Emanuele Bodon, Bodon, Emanuele
Mathematics · #11F85 #16E30 #16S15 #20C08 #20G25 #20J06 #22E50 #Advanced Operator Algebra Research #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.2405.00916
openalex publication_date 2024/05/02 · openalex created_date 2024/05/05 · openalex updated_date 2026/07/28
The pro-p Iwahori-Hecke Ext-algebra E^∗ is a graded algebra that has been introduced and studied by Ollivier-Schneider, with the long-term goal of investigating the category of smooth mod-p representations of p-adic reductive groups and its derived category. Its 0th graded piece is the pro-p Iwahori-Hecke algebra studied by Vignéras and others. In the present article, we first show that the Ext-algebra E^∗ associated with the group SL2(\mathfrakF), PGL2(\mathfrakF) or GL2(\mathfrakF), where \mathfrakF is an unramified extension of ℚp with p ≠ 2,3, is finitely generated as a (non-commutative) algebra. We then specialize to the case of the group SL2(ℚp), with p ≠ 2,3, and we show that in this case the natural multiplication map from the tensor algebra T^∗E0 E1 to E^∗ is surjective and that its kernel is finitely generated as a two-sided ideal. Using this fact as main input, we then show that E^∗ is finitely presented as an algebra. We actually compute an explicit presentation.