Graded components of local cohomology modules of invariant rings. Issue 2 (1st February 2020)

• Record Type: Journal Article
• Authors: Puthenpurakal, Tony J.; Roy, Sudeshna
• Is Part Of: Communications in algebra. Volume 48:Issue 2(2020)
• Page Start: 803
• Page End: 814
• Publication Date: 2020-02-01
• Subjects: Graded local cohomology -- invariant rings -- local comohology; Primary 13D45 -- 14B15 -- Secondary 13A50 -- 32C36; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1662912
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let A be a regular domain containing a field K of characteristic zero, G be a finite subgroup of the group of automorphisms of A and B = A G be the ring of invariants of G . Let S = A [ X 1, …, X m ] and R = B [ X 1, …, X m ] be standard graded with deg A = 0, deg B = 0 and deg X i = 1 for all i . Extend the action of G on A to S by fixing Xi . Note S G = R . Let I be an arbitrary homogeneous ideal in R . The main goal of this paper is to establish a comparative study of graded components of local cohomology modules H I i ( R ) that would be analogs to those proven in the paper [5 ] for H J i ( S ) where J is an arbitrary homogeneous ideal in S .