Logo image
Galois structure of homogeneous coordinate rings
Journal article   Open access   Peer reviewed

Galois structure of homogeneous coordinate rings

Frauke M. Bleher and Ted Chinburg
Transactions of the American Mathematical Society, Vol.360(12), pp.6269-6301
12/2008
DOI: 10.1090/S0002-9947-08-04436-X
url
https://doi.org/10.1090/S0002-9947-08-04436-XView
Published (Version of record) Open Access

Abstract

Suppose G is a finite group acting on a projective scheme X over a commutative Noetherian ring R. We study the RG-modules H0(X, F⊗Ln) when n ≥ 0, and F and L are coherent G-sheaves on X such that L is an ample line bundle. We show that the classes of these modules in the Grothendieck group G0(RG) of all finitely generated RG-modules lie in a finitely generated subgroup. Under various hypotheses, we show that there is a finite set of indecomposable RG-modules such that each H0(X, F⊗Ln) is a direct sum of these indecomposables, with multiplicities given by generalized Hilbert polynomials for n >> 0
Research article

Details

Metrics

Logo image