Lattices and cohomological Mackey functors for finite cyclic p-groups
Category Theory
2012-09-11 v1 Representation Theory
Abstract
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).
Keywords
Cite
@article{arxiv.1209.1932,
title = {Lattices and cohomological Mackey functors for finite cyclic p-groups},
author = {Blas Torrecillas and Thomas Weigel},
journal= {arXiv preprint arXiv:1209.1932},
year = {2012}
}