Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 1 (2013), 1-18.
Powers of ideals and the cohomology of stalks and fibers of morphisms
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.
Algebra Number Theory, Volume 7, Number 1 (2013), 1-18.
Received: 22 June 2010
Revised: 10 January 2012
Accepted: 7 February 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13D45: Local cohomology [See also 14B15] 14A15: Schemes and morphisms
Chardin, Marc. Powers of ideals and the cohomology of stalks and fibers of morphisms. Algebra Number Theory 7 (2013), no. 1, 1--18. doi:10.2140/ant.2013.7.1. https://projecteuclid.org/euclid.ant/1513729927