Back to Departmental Colloquium: Fall 2010
Departmental Colloquium
Date: Thursday, Oct 28, 2010
Time: 4:15PM
Location: JWB 335
Gennady Lyubeznik
University of Minnesota
Title |
Characteristic-free aspects of the theory of D-modules |
Abstract |
The theory of rings of differential operators and modules over them exists mostly in characteristic zero. Only some isolated results are known in characteristic p>0. Some characteristic zero results are known to be false in characteristic p>0. Even those results that hold both in characteristic zero and in characteristic p>0 often have very different proofs in these two cases. Very recently Vladimir Bavula found a characteristic-free definition of a fundamental characteristic zero concept - that of holonomic D-modules - and showed that his holonomic modules have some of the striking properties that make holonomic modules so useful in characteristic zero (in characteristic zero Bavula’s definition coincides with the usual one). This discovery has since been used to give the first characteristic-free proof of a very basic fact about D-modules which had been proven earlier by two completely different methods in characteristic zero and in characteristic p>0. Study of Bavula’s holonomic modules is ongoing. We will survey these developments in the talk. |
Commutative Algebra