Galois structure of homogeneous coordinate rings
| dc.creator | Bleher, Frauke M. | |
| dc.creator | Chinburg, Ted | |
| dc.date | 2005-04-13 | |
| dc.date | 2006-07-22 | |
| dc.date.accessioned | 2026-07-07T12:21:18Z | |
| dc.date.available | 2026-07-07T12:21:18Z | |
| dc.description | Suppose $G$ 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.description | 27 pages. The abstract and introduction have been changed; the article has been shortened | |
| dc.identifier | https://arxiv.org/abs/math/0504281 | |
| dc.identifier | http://arxiv.org/abs/math/0504281 | |
| dc.identifier | Trans. Amer. Math. Soc. 360 (2008), no. 12, 6269-6301. | |
| dc.identifier | doi:10.1090/S0002-9947-08-04436-X | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213324 | |
| dc.subject | Group Theory | |
| dc.subject | Number Theory | |
| dc.subject | 20C05; 14L30; 14C40; 13A50 | |
| dc.title | Galois structure of homogeneous coordinate rings | |
| dc.type | text |