TL;DR
This paper introduces a method for determining the upper bound of module complexity over local rings by analyzing cohomology vanishing, with a focus on complete intersections where all modules have finite complexity.
Contribution
It provides a new approach to compute complexity bounds using cohomology vanishing, specifically applied to complete intersection rings.
Findings
Established a method to compute upper bounds of module complexity
Characterized complete intersections as rings where all modules have finite complexity
Connected cohomology vanishing to module complexity bounds
Abstract
A method is provided for computing an upper bound of the complexity of a module over a local ring, in terms of vanishing of certain cohomology modules. We then specialize to complete intersections, which are precisely the rings over which all modules have finite complexity.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Rings, Modules, and Algebras