Hecke Operators on Stable Cohomology

2013/11/20 by Frank Calegari, Calegari, Frank, Matthew Emerton +1
Mathematics · #11F75 #11F80 #19F99 #FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT) #math.GT #math.NT #msc:11F75 #msc:11F80 #msc:19F99

paper · pdf · doi:10.48550/arxiv.1311.5183

arxiv created 2013/11/20 · arxiv updated 2013/11/21

Abstract

We prove that the completed cohomology groups of SL_N(Z) in fixed degree stabilize as N goes to infinity. We also prove that the action of Hecke operators on stable cohomology is trivial, in a precisely defined sense.

Related

• The Stable Homology of Congruence Subgroups
• Stable cohomology of congruence subgroups
• Stability in Bounded Cohomology for Classical Groups, I: The Symplectic Case
• Cohomology at Infinity and the Well-Tempered Complex
• Stable models of Hecke operators