Homology of twisted quiver bundles with relations
arXiv:1806.04697 · doi:10.1016/j.jalgebra.2019.10.044
Abstract
We study the Ext modules in the category of left modules over a twisted algebra of a finite quiver over a ringed space , allowing for the presence of relations. We introduce a spectral sequence which relates the Ext modules in that category with the Ext modules in the category of -modules. Contrary to what happens in the absence of relations, this spectral sequence in general does not degenerate at the second page. We also consider local Ext sheaves. Under suitable hypotheses, the Ext modules are represented as hypercohomology groups
24 pages, 1 figure. v2: 23 pages, 1 figure; last section rewritten with a shorter and more direct proof; references added. v3: Corrections in the metadata. v4: Typos corrected; Lemma 2.3 needed slightly stronger hypotheses. v5: The exposition has been thoroughly streamlined and an example has been added. 22 pages