Geodesic
Big Cohen-Macaulay Modules, Morphisms of Perfect Complexes, and Intersection Theorems in Local Algebra
Documenta mathematica, Tome 23 (2018), pp. 1601-1619.

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

There is a well known link from the first topic in the title to the third one. In this paper we thread that link through the second topic. The central result is a criterion for the tensor nilpotence of morphisms of perfect complexes over commutative noetherian rings, in terms of a numerical invariant of the complexes known as their level. Applications to local rings include a strengthening of the Improved New Intersection Theorem, short direct proofs of several results equivalent to it, and lower bounds on the ranks of the modules in every finite free complex that admits a structure of differential graded module over the Koszul complex on some system of parameters.
Classification : 13D22, 13D02, 13D09
Keywords: big Cohen-Macaulay module, homological conjectures, level, perfect complex, rank, tensor nilpotent morphism 
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Avramov, Luchezar L.; Iyengar, Srikanth B.; Neeman, Amnon. Big Cohen-Macaulay Modules, Morphisms of Perfect Complexes, and Intersection Theorems in Local Algebra. Documenta mathematica, Tome 23 (2018), pp. 1601-1619. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a18/