|Speaker:||Takehiko Yasuda (Osaka U)|
|Title:||Motivic integration and the p-cyclic McKay correspondence|
|Date (JST):||Mon, Aug 27, 2012, 14:00 - 17:00|
|Place:||Seminar Room A|
I will talk about the McKay correspondence for the cyclic group of order p in characteristic p. The main tool is the motivic integration generalized to quotient stacks associated to representations. A consequence is that a crepant resolution of the quotient variety has topological Euler characteristic p like in characteristic zero. Of course, we will find some new features which did not appear in characteristic zero. For instance, the number of rational points of a crepant resolution is related to a weighted count of Artin-Schreier extensions of the power series field.
In the first part of the talk, I will briefly review the motivic integration theory. Then I will outline my results with emphasis on a comparison with results in characteristic zero.
In the second part of the talk, I will explain in more details the motivic integration generalized to the quotient stack associated to a p-cyclic representation.