Castelnuovo-Mumford regularity over general base rings

Abstract: Our talk has two goals. The first is to give a short introduction to Castelnuovo-Mumford regularity for standard graded rings over general base rings. The second is to present a simple and concise proof of a classical result of Cutkosky, Herzog and Trung and, independently, Kodiyalam asserting that the regularity of powers of a homogeneous ideal is eventually a linear function of the exponent in this generality. Finally we show how the flexibility of working over general base rings can be used to give a simple proof for the characterization of "linear powers" in terms of the Rees algebra.

This is joint work with Aldo Conca and Matteo Varbaro. See "Castelnuovo-Mumford regularity and powers", arXiv:2107.14734. An extensive version will be part of the forthcoming book "Determinants, Gröber bases and cohomology" with Conca, Varbaro and Claudiu Raicu.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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