On the Frobenius closure of parameter ideals when the ring is F-injective on the punctured spectrum

2022/09/28 by Dương Thị Hương, Huong, Duong Thi, Phạm Hùng Quý +1
Mathematics · #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2209.13872

Abstract

Let (R,\frak m) be an excellent generalized Cohen-Macaulay local ring of dimension d that is F-injective on the punctured spectrum. Let \frak q be a standard parameter ideal of R. The aim of the paper is to prove that ℓ_R(\frak q^F/\frak q)≤ ∑_i=0^d\binomdiℓ_R(0^F_Hⁱ_{\frak m}(R)). Moreover, if \frak q is contained in a large enough power of \frak m, we have \frak q^F/\frak q ≅ \bigoplus_i=0^d (0^F_Hⁱ_{\frak m}(R))^\binomdi.

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