The saturation of Frobenius powers of ideals
Craig Huneke
TL;DR
This paper investigates the behavior of Frobenius powers of ideals, focusing on localization of tight closure and the LC condition related to local cohomology bounds in quotient rings.
Contribution
It establishes specific cases where localization of tight closure holds and analyzes the LC condition concerning Frobenius iterates.
Findings
Localization of tight closure holds in certain special cases
Bounds on Loewy lengths of local cohomology are studied
Conditions under which Frobenius powers behave predictably
Abstract
This paper proves some special cases in which localization of tight closure holds. In particular it studies the condition LC relating to bounding the Loewy lengths of local cohomology of Frobenius iterates of quotient rings.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Algebraic Geometry and Number Theory