Back to Commutative Algebra Seminar: Spring 2015
Commutative Algebra Seminar
Date: Friday, Jan 30, 2015
Time: 3:10PM - 4:00PM
Location: LCB 222
Nick Switala
University of Minnesota
Title |
Matlis duality for D-modules and de Rham cohomology |
Abstract |
Let R be a formal power series ring over a field k of characteristic zero, and let D be the ring of k-linear differential operators on R. By interpreting the Matlis dual of an R-module M in terms of certain k-linear maps from M to k (following SGA2), we show that given any left D-module, there is a natural structure of left D-module on its Matlis dual, whose de Rham cohomology is k-dual to that of the original module in the holonomic case. We then give an application to Hartshorne’s theory of de Rham homology and cohomology for R, showing that the associated Hodge-de Rham spectral sequences (beginning with their E_2 terms) are independent of the embedding used in their definition and consist of finite-dimensional k-spaces. |
Commutative Algebra