On the associated primes of local cohomology
Hailong Dao, Pham Hung Quy

TL;DR
This paper proves finiteness of associated primes of local cohomology modules in certain rings of positive characteristic, extending previous results and providing criteria related to singularities for finiteness in all characteristics.
Contribution
It offers a new, concise proof for finiteness of associated primes in rings with finite $F$-representation type or finite singular locus, and establishes criteria linking singularities to associated prime finiteness.
Findings
Finiteness of associated primes for local cohomology in rings with finite $F$-representation type.
Extension of previous results by Takagi-Takahashi.
Criteria relating singularities to finiteness of associated primes in all characteristics.
Abstract
Let be a commutative Noetherian ring of prime characteristic . In this paper we give a short proof using filter regular sequences that the set of associated prime ideals of is finite for any ideal and for any when has finite -representation type or finite singular locus. This extends a previous result by Takagi-Takahashi and gives affirmative answers for a problem of Huneke in many new classes of rings in positive characteristic. We also give a criterion about the singularities of (in any characteristic) to guarantee that the set of associated primes of is always finite.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models
