Tahehiko Yasuda: Motivic integration over DM stacks and its applications (ZOOM; Mittagsseminar zur Arithmetik)
Dienstag, 30.06.2020 10:15
Abstract: I will talk about the theory of motivic integration over DM stacks. This theory originates in the proof of a version of the McKay correspondence by Denef and Loeser by means of motivic integration. I have been working on generalization of the McKay correspondence and motivic integration over DM stacks to the wild situation for these years. Here "wild" means that relevant finite groups may have order divisible by the characteristic of the field. Recently I was able to construct the desired theory in a rather general setting in the case of equal characteristics. The key ingredients were the moduli space of torsors over the punctured formal disk constructed in my joint work with F. Tonini and the untwisting technique in terms of Hom stacks. As applications, we get the wild McKay correspondence for arbitrary finite groups and the motivic version of Bhargava's mass formula.