DOCUMENTA MATHEMATICA, Vol. 22 (2017), 1593-1614

Hailong Dao, William T. Sanders

Cohomological Support and the Geometric Join

Let $M,N$ be finitely generated modules over a local complete intersection $R$. Assume that all the modules $\torRi(M,N)$ are zero for $i>0$. We prove that the cohomological support of $M\otimesR N$ (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.