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تسجيل مستخدم جديدAsymptotic linear bounds of Castelnuovo-Mumford regularity in multigraded modules
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Dipankar Ghosh
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Let $A$ be a Noetherian standard $mathbb{N}$-graded algebra over an Artinian local ring $A_0$. Let $I_1,ldots,I_t$ be homogeneous ideals of $A$ and $M$ a finitely generated $mathbb{N}$-graded $A$-module. We prove that there exist two integers $k$ and $k$ such that [ mathrm{reg}(I_1^{n_1} cdots I_t^{n_t} M) leq (n_1 + cdots + n_t) k + k quadmbox{for all }~n_1,ldots,n_t in mathbb{N}. ]
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This note has two goals. The first is to give a short and self contained introduction to the Castelnuovo-Mumford regularity for standard graded ring $R$ over a general base ring. The second is to present a simple and concise proof of a classical resu
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