Unbounding Ext

2011/01/15 by David I. Stewart, Stewart, David I.
Mathematics · Social Sciences · #FOS: Mathematics #Gender Studies in Language #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.GR #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.1101.3004

14 pages; version to appear in J. Alg

openalex publication_date 2011/01/15 · arxiv created 2012/08/30 · arxiv updated 2012/08/31 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We produce examples in the cohomology of algebraic groups which answer two questions of Parshall and Scott. Specifically, if G=SL₂, then we show: (a) dim \Ext_G²(L,L) can be arbitrarily large for a simple module L; and (b) the sequence max_L-irreddim H^k(G,L) grows exponentially fast with k.

Related

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• Bounding Ext for modules for algebraic groups, finite groups, and quantum groups
• Unconditional bounds for the multiplicity of automorphic forms of cohomological type on GL₂
• Asymptotic syzygies grow exponentially: a remark on a paper of Ein-Lazarsfeld
• On The Cohomology of SL₂ with Coefficients in a Simple Module