On the behavior of stringy motives under Galois quasi-étale covers

To a log-terminal singularity, we may attach a stringy motive.  I will explain the strict descent of such stringy motives under ramified Galois quasi-étale covers in between log-terminal singularities of dimension at most 3. The comparison between stringy motives is done via their Poincaré realizations. Such strict descent reduces the problem regarding the finiteness of the local étale fundamental group of log terminal singularities to a descending chain condition (DCC) for stringy motives. I will show such DCC to hold in dimension 2. In particular, I will give a characteristic-free proof for the finiteness of the local étale fundamental group of log-terminal surface singularities, which was open in characteristics 2 and 3. This is all joint work with Takehiko Yasuda from Osaka University.