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2013 Powers of ideals and the cohomology of stalks and fibers of morphisms
Marc Chardin
Algebra Number Theory 7(1): 1-18 (2013). DOI: 10.2140/ant.2013.7.1


We first provide here a very short proof of a refinement of a theorem of Kodiyalam and Cutkosky, Herzog and Trung on the regularity of powers of ideals. This result implies a conjecture of Hà and generalizes a result of Eisenbud and Harris concerning the case of ideals primary for the graded maximal ideal in a standard graded algebra over a field. It also implies a new result on the regularities of powers of ideal sheaves. We then compare the cohomology of the stalks and the cohomology of the fibers of a projective morphism to the effect of comparing the maximums over fibers and over stalks of the Castelnuovo–Mumford regularities of a family of projective schemes.


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Marc Chardin. "Powers of ideals and the cohomology of stalks and fibers of morphisms." Algebra Number Theory 7 (1) 1 - 18, 2013.


Received: 22 June 2010; Revised: 10 January 2012; Accepted: 7 February 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1270.13008
MathSciNet: MR3037888
Digital Object Identifier: 10.2140/ant.2013.7.1

Primary: 13D02
Secondary: 13A30 , 13D45 , 14A15

Keywords: Castelnuovo–Mumford regularity , Cohomology , fibers of morphisms , powers of ideals , Rees algebras , stalks

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 1 • 2013
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