Time: 15:30-16:30, Monday, July 29

Venue: Lecture Hall

Abstract: (Topological) Euler characteristic of crepant resolutions plays an important role in study of McKay correspondence. Over complex numbers, it is known as the generalized McKay correspondence that for a finite subgroup of SL(n), if its associated quotient singularity has a crepant resolution, then the Euler characteristic of crepant resolution equals the number of conjugacy classes of the finite group. However, the analog of the generalized McKay correspondence may fail in characteristic p when the group is modular (which means that its order is divided by p). Therefore, a different formula of Euler characteristic of crepant resolutions in positive characteristic is wanted. In this talk, we will introduce several examples of crepant resolutions in positive characteristic and approaches to compute Euler characteristics of some specific kinds of crepant resolutions of modular quotient singularities.