A note on the depth formula and vanishing of cohomology
Arash Sadeghi
TL;DR
This paper investigates conditions under which the depth formula holds for modules over local rings, focusing on modules with reducible complexity and finite Gorenstein dimension, and explores vanishing of cohomology for modules with finite complete intersection dimension.
Contribution
It establishes new conditions ensuring the validity of the depth formula for modules with specific homological properties over local rings.
Findings
Depth formula holds when one module has reducible complexity and finite Gorenstein dimension with vanishing Tor.
Vanishing of cohomology is studied for modules with finite complete intersection dimension.
Results extend understanding of homological behavior of modules over local rings.
Abstract
It is proved that if one of the finite modules M and N, over a local ring R, has reducible complexity and has finite Gorenstein dimension then the depth formula holds, provided TorR_i(M,N) = 0 for i>>0. We also study the vanishing of cohomology of a module of finite complete intersection dimension.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics