2011/04/10 by Dieter Degrijse, Degrijse, Dieter, Nansen Petrosyan +1
Mathematics · #11R34 #18G60 #55N99 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.AT #math.CT #math.GR #math.NT #msc:11R34 #msc:18G60 #msc:55N99
paper · pdf · doi:10.48550/arxiv.1104.1766
39 pages
arxiv created 2011/04/10 · openalex publication_date 2011/04/10 · arxiv updated 2011/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be an arbitrary family of subgroups of a group G and let Orb be the associated orbit category. We investigate interpretations of low dimensional F-Bredon cohomology of G in terms of abelian extensions of Orb. Specializing to fixed point functors as coefficients, we derive several group theoretic applications and introduce Bredon-Galois cohomology. We prove an analog of Hilbert's Theorem 90 and show that the second Bredon-Galois cohomology is a certain intersection of relative Brauer groups. As applications, we realize the relative Brauer group Br(L/K) of a finite separable non-normal extension of fields L/K as a second Bredon cohomology group and show that this approach is quite suitable for finding nonzero elements in Br(L/K).