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Article overview
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G-graded Castelnuovo Mumford Regularity | | Nicolás Botbol
; Marc Chardin
; | | Date: |
13 Jul 2011 | | Abstract: | We develop a general graded variant of Castelnuovo-Mumford regularity for
modules over a commutative ring $R$ graded by a finitely generated abelian
group $G$. With this aim, we establish a clear relation between supports of
local cohomology modules and supports of Tor modules and Betti numbers. We give
a definition of weak and very weak $gamma$-regularity, as well as an extension
of the notion of Castelnuovo-Munford regularity which is closely related to
previous ones. We provide new stability results for these regularity regions.
We extend results on Hilbert function to multigraded polynomial rings. In
particular, we prove that for a finitely generated module, by
Grothendieck-Serre formula, there is a numerical polynomial that coincides with
its Hilbert function in the regularity region. | | Source: | arXiv, 1107.2494 | | Services: | Forum | Review | PDF | Favorites | |
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