2007/02/04 by Joseph Lipman, Lipman, Joseph · 1 citation
Mathematics · #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.math/0702082
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).