English

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.

Keywords

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

R2 v1 2026-06-21T21:59:19.672Z