Time：16:45-17:45, Friday, March 21 2025
Venue：E4-233
Speaker: Yigeng Zhao, ITS
Title：Cohomological approach to geometric ramification theory
Abstract:
For a constructible étale sheaf on a variety of positive characteristic p, there are two globally defined invariants: Euler-Poincaré characteristic and epsilon factor, which appear in the functional equation of its Grothendieck L-function. We study their relationships with locally defined ramification invariants of the sheaf in geometric ramification theory. Those local invariants are usually treated as numbers or 0-cycles, while we show they share nice functorial properties as cohomological classes in this talk. As applications, we confirm Kato-Saito's conjecture on the twist formula for epsilon factors and the quasi-projective case of Saito's conjecture on characteristic classes.
