A vanishing theorem for finitely supported ideals in regular local rings
Commutative Algebra
2007-05-23 v2 Algebraic Geometry
Abstract
A cohomological vanishing property is proved for finitely supported ideals in an arbitrary d-dimensional regular local ring. (Such vanishing implies some refined Briancon-Skoda-type results, not otherwise known in mixed characteristic.) It follows that the adjoint of a finitely supported ideal I of order a has order sup(a+1-d, 0), and that taking adjoints of finitely supported ideals commutes with taking strict transforms at infinitely near points. In particular, the adjoint of I is also finitely supported. Also: if this I is a normal ideal, then its reduction number is the least integer > d(1-1/a).
Cite
@article{arxiv.math/0702082,
title = {A vanishing theorem for finitely supported ideals in regular local rings},
author = {Joseph Lipman},
journal= {arXiv preprint arXiv:math/0702082},
year = {2007}
}
Comments
12 pages. Main results and proofs similar to previous version, but with numerous enhancements