Galois structure of homogeneous coordinate rings

dc.creatorBleher, Frauke M.
dc.creatorChinburg, Ted
dc.date2005-04-13
dc.date2006-07-22
dc.date.accessioned2026-07-07T12:21:18Z
dc.date.available2026-07-07T12:21:18Z
dc.descriptionSuppose $G$ is a finite group acting on a projective scheme $X$ over a commutative Noetherian ring $R$. We study the $RG$-modules $\HH^0(X,\mathcal{F} \otimes \mathcal{L}^n)$ when $n \ge 0$, and $\mathcal{F}$ and $\mathcal{L}$ are coherent $G$-sheaves on $X$ such that $\mathcal{L}$ is an ample line bundle. We show that the classes of these modules in the Grothendieck group $G_0(RG)$ 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 $\HH^0(X,\mathcal{F} \otimes \mathcal{L}^n)$ is a direct sum of these indecomposables, with multiplicites given by generalized Hilbert polynomials for $n >> 0$.
dc.description27 pages. The abstract and introduction have been changed; the article has been shortened
dc.identifierhttps://arxiv.org/abs/math/0504281
dc.identifierhttp://arxiv.org/abs/math/0504281
dc.identifierTrans. Amer. Math. Soc. 360 (2008), no. 12, 6269-6301.
dc.identifierdoi:10.1090/S0002-9947-08-04436-X
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/213324
dc.subjectGroup Theory
dc.subjectNumber Theory
dc.subject20C05; 14L30; 14C40; 13A50
dc.titleGalois structure of homogeneous coordinate rings
dc.typetext

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