Cohomological Support and the Geometric Join

Let $M,N$ be finitely generated modules over a local complete intersection
$R$. Assume that all the modules $\tor^{R}_{i}(M,N)$ are zero for $i>0$. We
prove that the cohomological support of $M\otimes_{R} N$ (in the sense of
Avramov-Buchweitz) is equal to the geometric join of the cohomological
supports of $M,N$. This result gives a new connection between two active
areas or research, and immediately produces several interesting corollaries.
Naturally, it also raises many intriguing new questions about the homological
properties of modules over a complete intersection, some of which are investigated
in this work. 2010 MSC Classification: 13D07

2010 Mathematics Subject Classification:

Keywords and Phrases:

Full text: dvi.gz 38 k, dvi 94 k, ps.gz 297 k, pdf 210 k.

Home Page of DOCUMENTA MATHEMATICA