2020/07/14 by Jon F. Carlson, Jon Carlson, Carlson, Jon F.
Chemistry · Mathematics · #20C20 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Chemistry #Cohomology #Cohomology ring #Commutative Algebra and Its Applications #Computer science #Discrete mathematics #Endomorphism #Endomorphism ring #Equivariant cohomology #Extension (predicate logic) #FOS: Mathematics #Geometry #Group (periodic table) #Group cohomology #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum mechanics #Representation Theory (math.RT) #Ring (chemistry) #Scheme (mathematics) #Square (algebra) #Zero (linguistics) #math.RT #msc:20C20
paper · pdf · doi:10.48550/arxiv.2007.07305
arxiv created 2020/07/14 · openalex publication_date 2020/07/14 · arxiv updated 2020/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let k be a field of characteristic 2 and let H be a finite group or group scheme. We show that the negative Tate cohomology ring \widehatH≤ 0(H,k) can be realized as the endomorphism ring of the trivial module in a Verdier localization of the stable category of kG-modules for G an extension of H. This means in some cases that the endomorphism of the trivial module is a local ring with infinitely generated radical with square zero. This stands in stark contrast to some known calculations in which the endomorphism ring of the trivial module is the degree zero component of a localization of the cohomology ring of the group.