2012/09/10 by Blas Torrecillas, B. Torrecillas, Torrecillas, Blas +2 · 3 citations
Mathematics · #18A25 #20C11 #20J06 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings, Modules, and Algebras #math.CT #math.RT #msc:18A25 #msc:20C11 #msc:20J06
paper · pdf · doi:10.48550/arxiv.1209.1932
arxiv created 2012/09/10 · openalex publication_date 2012/09/10 · arxiv updated 2012/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a finite cyclic p-group G and a discrete valuation domain R of characteristic 0 with maximal ideal pR the R[G]-permutation modules are characterized in terms of the vanishing of first degree cohomology on all sub- groups (cf. Thm. A). As a consequence any R[G]-lattice can be presented by R[G]-permutation modules (cf. Thm. C). The proof of these results is based on a detailed analysis of the category of cohomological G-Mackey functors with values in the category of R-modules. It is shown that this category has global dimension 3 (cf. Thm. E). A crucial step in the proof of Theorem E is the fact that a gentle R-order category (with parameter p) has global dimension less or equal to 2 (cf. Thm. D).