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Computing Local Cohomology of Polynomial Rings of Characteristic Zero

Commutative Algebra and its Interaction with Algebraic Geometry (Notre Dame) May 22, 2023 - June 02, 2023

June 01, 2023 (02:30 PM PDT - 03:30 PM PDT)
Speaker(s): Uli Walther (Purdue University)
Video

Computing Local Cohomology Of Polynomial Rings Of Characteristic Zero

Abstract

Suppose R=KK[x_1,...,x_n] is a polynomial ring over a field KK of characteristic zero. If I is an ideal in R, then the local cohomology modules H^j_I(R) can be computed (at least in principle) in Macaulay2. In this talk we discuss the basic ideas that go into this (Groebner basis driven) algorithm. This involves a tour through the land of D-modules, with specific focus on the concept of Bernstein—Sato polynomials attached to elements f of R (which we will define and discuss).

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Computing Local Cohomology Of Polynomial Rings Of Characteristic Zero

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