348 research outputs found
Asymptotic linear bounds of Castelnuovo-Mumford regularity in multigraded modules
Let be a Noetherian standard -graded algebra over an Artinian
local ring . Let be homogeneous ideals of and a
finitely generated -graded -module. We prove that there exist
two integers and such that \mathrm{reg}(I_1^{n_1} \cdots I_t^{n_t}
M) \leq (n_1 + \cdots + n_t) k + k'
\quad\mbox{for all }~n_1,\ldots,n_t \in \mathbb{N}. Comment: 9 page
A short proof of a result of Katz and West
We give a short proof of a result due to Katz and West: Let be a
Noetherian ring and ideals of . Let and be finitely
generated -modules and a submodule. For every fixed , the sets and are independent of
for all sufficiently large .Comment: 3 pages, revised versio
The (ir)regularity of Tor and Ext
We investigate the asymptotic behaviour of Castelnuovo-Mumford regularity of
Ext and Tor, with respect to the homological degree, over complete intersection
rings. We derive from a theorem of Gulliksen a linearity result for the
regularity of Ext modules in high homological degrees. We show a similar result
for Tor, under the additional hypothesis that high enough Tor modules are
supported in dimension at most one; we then provide examples showing that the
behaviour could be pretty hectic when the latter condition is not satisfied.Comment: 24 pages, Comments and suggestions are welcom
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