We introduce finite and linearly reductive group schemes over fields, their actions on affine space, and the associated quotient singularities. The main goal is to establish a McKay correspondence for finite and linearly reductive subgroup schemes of SL_2 over algebraically closed fields of positive characteristic. As an application, we obtain a McKay correspondence for all rational double point singularities in characteristic different from 2,3,5. If time permits, we will briefly discuss non-commutative crepant resolutions (in the sense of van den Bergh) of these singularities, as well as work in progress of all of this over fields that are not algebraically closed. Part of these results are joint work with Gebhard Martin, Yuya Matsumoto, Matthew Satriano, and Takehiko Yasuda.
A McKay Correspondence in Positive Characteristic
25.03.2025 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: