2025/11/08 by Sayed Sadiqul Islam, Islam, Sayed Sadiqul
Computer Science · Mathematics · #13H10 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13D45 #Rings, Modules, and Algebras #Secondary 13N10
paper · pdf · doi:10.48550/arxiv.2511.05871
openalex publication_date 2025/11/08 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28
For a Noetherian commutative ring R, let HiI(R) be the i-th local cohomology module of R with respect to I. In \citeHel-08, Hellus posed the question of identifying rings R such that injdimR HiI(R)=dimR(SuppR HiI(R)). In this paper, we show that a regular affine domain over a field of characteristic 0 satisfies this condition. In fact, we prove that injdimR HiI(R)≥ dimR(SuppR HiI(R))-1 when R is a differentiably admissible K-algebra. Indeed, we establish both of these conclusions for a substantially broad class of functors known as Lyubeznik functors. We also prove that if R is a polynomial ring over a differentiably admissible K-algebra, then AssR HiI(R) is finite for all i≥ 0 and for every ideal I of R.