Geodesic
Cohomological Support and the Geometric Join
Documenta mathematica, Tome 22 (2017), pp. 1593-1614.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 13D07
Keywords: cohomological support 
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     author = {Dao, Hailong and Sanders, William T.},
     title = {Cohomological {Support} and the {Geometric} {Join}},
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Dao, Hailong; Sanders, William T. Cohomological Support and the Geometric Join. Documenta mathematica, Tome 22 (2017), pp. 1593-1614. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a4/