Doosung Park: Motivic six-functor formalism for log scheme

Abstract

In this talk, I will explain a work in progress about the construction of the stable motivic homotopy categories of fine saturated log schemes and their motivic six-functor formalism. This includes the construction of the exceptional push-forward functor, the Poincaré duality, and a special case of the Lefschetz duality. As an application, I will show that the motivic semistable degeneration is independent of the choice of relative compactifications, and I will present the motive of the degenerated torus as an MZ-module over the log point.