Associate primes of local cohomology modules over certain quotients of regular rings

2025/03/26 by Puthenpurakal, Tony J.
#13A30 #14B15 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13D45 #Secondary 13N10

paper · doi:10.48550/arxiv.2503.20539

Abstract

Let R be a regular ring containing a field k. Let x = x₁, …, x_r be a regular sequence in R such that R/(x) is a regular ring. Fix m ≥ 1. Set A_m = R/(x)^m. We show that for any ideal Q of A_m the set Ass Hⁱ_Q(A_m) is a finite set for i ≥ 0, in the following cases: 1. char k = p > 0. 2. char k = 0, R is local or a smooth affine algebra over k.

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