A uniform Chevalley theorem for direct summands in mixed characteristic

Abstract: Let R be a graded direct summand of a positively graded polynomial ring over the p-adic integers. We exhibit an explicit constant D such that, for any positive integer n and any homogeneous prime ideal Q of R, the Dn-th symbolic power of Q is contained in the n-th power of the homogeneous maximal ideal (p)R + R_+. The strategy relies on the introduction of a new type of differential powers, which do not require the existence of a p-derivation on R. The talk will be based on joint work with E. Grifo and J. Jeffries.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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