The wild McKay correspondence, which is a variant of the McKay correspondence in positive characteristics, shows that stringy motives of quotient varieties equal some motivic integrals. However, it is not easy to compute the integrals in general. In this talk, we compute them for the cyclic groups of prime power order case. Especially, we give a criterion whether the stringy motives converges or not. We can apply it to study singularities. For instance, it is well-known that if the stringy motive converges, the quotient is canonical.
(Some results in this talk are joint work with Takehiko Yasuda).
(This is a talk of Tokyo-Kyoto AG seminar on Zoom, and will be given in Japanese.)