Cohomological Support and the Geometric Join

Hailong Dao, William Sanders
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 ⊗ 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
more » ... ons about the homological properties of modules over a complete intersection, some of which are investigated in this work. 2010 MSC Classification: 13D07