Cohomological length functions
Representation Theory
2013-05-22 v3 Category Theory
K-Theory and Homology
Abstract
We study certain integer valued length functions on triangulated categories and establish a correspondence between such functions and cohomological functors taking values in the category of finite length modules over some ring. The irreducible cohomological functions form a topological space. We discuss its basic properties and include explicit calculations for the category of perfect complexes over some specific rings.
Cite
@article{arxiv.1209.0540,
title = {Cohomological length functions},
author = {Henning Krause},
journal= {arXiv preprint arXiv:1209.0540},
year = {2013}
}
Comments
17 pages. Version 2: Thorougly revised and extended version. A reference for Theorem 1.1 is included and the space of cohomological functions is now discussed in great detail. Version 3: Slightly revised version, providing few more details. Conjecture 4.8 included. One reference added