A vanishing theorem for finitely supported ideals in regular local rings

Details A vanishing theorem for finitely supported ideals in regular local rings A vanishing theorem for finitely supported ideals in regular local rings

2007-02-04

arxiv.org/abs/math/0702082v2

Mathematics

Commutative Algebra

12 pages. Main results and proofs similar to previous version, but with numerous enhancements

Scientific paper

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).

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