Local cohomology of modular invariant rings

2023/06/25 by Goel, Kriti, Jeffries, Jack, Singh, Anurag K. · 1 citation
#13A50 (Primary) #13B05 (Secondary) #13D45 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.14279

Abstract

For K a field, consider a finite subgroup G of GL_n(K) with its natural action on the polynomial ring R:=K[x₁,…,x_n]. Let \mathfrakn denote the homogeneous maximal ideal of the ring of invariants R^G. We study how the local cohomology module Hⁿ_\mathfrakn(R^G) compares with Hⁿ_\mathfrakn(R)^G. Various results on the a-invariant and on the Hilbert series of Hⁿ_\mathfrakn(R^G) are obtained as a consequence.

Cited by

• Homological properties of invariant rings of permutation groups

Related

• Graded components of local cohomology modules over invariant rings-II
• On the local cohomology of modular invariants
• Graded components of local cohomology modules of invariant rings
• Local cohomology with support in ideals of maximal minors
• On Invariants and Endomorphism Rings of Local Cohomology Modules