Quasi-unipotent motives and monodromic nearby cycles functor

Thời gian: 16h30 thứ năm, ngày 27/04

Địa điểm: Pòng 612, Nhà A6.

Link online: https://meet.google.com/yep-kbzk-eao?pli=1&authuser=4

Tóm tắt: In this talk we recall the construction of the motivic stable homotopy category of V. Voevodsky and F. Morel. During 2001-02, Voevodsky gave a full lecture at IAS on the formalism of six operations in the motivic world but never published the details. Later, J. Ayoub figured out the details and published in his thesis, we would like to present some basic building blocks of this formalism. In a later work (the second volume of the thesis) of J. Ayoub, he successfully constructed the so-called motivic nearby cycles functor based on an idea of Rapoport-Zink on proving the tameness of the étale nearby cycles for semi-stable schemes over a strict local trait. Using this construction, F. Ivorra and J. Sebag proved that the motivic nearby cycles functor is really a motivic incarnation of the motivic nearby cycles and motivic Milnor fibers derived from the limits of motivic zeta functions in the theory of motivic integration. We will discuss these together with the category of quasi-unipotent motives which is an updated version of the motivic stable homotopy category and then it allows us to bring the monodromy action into account, which is an indispensable feature of nearby cycles.