| Speaker: | Yudai Yamamoto (Osaka Univ.) |
|---|---|
| Title: | The space of twisted arc for the group scheme αp |
| Date (JST): | Thu, Nov 07, 2024, 15:30 - 17:00 |
| Place: | Balcony A |
| Abstract: |
Motivic integration is the useful tool for obtaining invariants of algebraic varieties by collecting infinitesimal curves called arcs, and This is known to have various ap- plications. For example, the classes of singularities of an algebraic variety are related to the convergence of a certain integral. The McKay correspondence via the motivic integration is the correspondence that a certain motivic integral on a quotient variety is represented by an integral consisting of information about the group. The McKay correspondence for the case where the group is a wild finite group was proved by Ya- suda, and the essential idea of the proof is to consider a variant of arcs called twisted arcs. In this talk, I will explain an explicit representation of the space of twisted arcs for the finite group scheme αp. And I will also explain the progress toward the McKay correspondence for αp by using the explicit representation, especially an attempt to change twisted arcs to ”ordinary” arcs. |
