A sufficient condition for strong 𝐹-regularity
Copyright policy )A sufficient condition for strong 𝐹-regularity
Let ( R , m , K ) (R,\mathfrak {m},K) be an F F -finite Noetherian local ring which has a canonical ideal I ⊊ R I \subsetneq R . We prove that if R R is S 2 S_2 and H m d − 1 ( R / I ) H^{d-1}_{\mathfrak {m}}(R/I) is a simple R { F } R\{F\} -module, then R R is a strongly F F -regular ring. In particular, under these assumptions, R R is a Cohen-Macaulay normal domain.
- University of Genoa Italy
- University of Virginia United States
- University of Virginia Main Campus United States
Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, canonical ideal, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 13, F-purity, tight closure, Local cohomology and commutative rings, F-regularity, F-rationality, FOS: Mathematics
Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, canonical ideal, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 13, F-purity, tight closure, Local cohomology and commutative rings, F-regularity, F-rationality, FOS: Mathematics
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