Introduction to motivic homotopy theory
Người báo cáo: Phạm Khoa Bằng (Rennes 1 University)

Thời gian: 16:30, thứ năm, 04/08/2022

Tóm tắt: The A^1-homotopy theory or motivic homotopy theory is the homotopy theory of smooth schemes, where the affine line A^1 plays the role of the unit interval in homotopy theory. In recent years, the development of this theory has led to important applications such as the proofs of the Milnor and Bloch-Kato conjectures due to V. Voevodsky. In this talk, we would like to review central notions in the theory. More specially, by using the language of model categories, we construct the motivic (unstable) stable homotopy theory SH(-) and use it to formulate motivic cohomology. The construction SH(-) is a typical example of a so-called stable homotopical 2-functor; given any such functor, one automatically has the formalism of six operations just as in l-adic cohomology. If time permits, we also introduce the category of étale motives over a ring (another example of a stable homotopical 2-functor), the nearby cycles functor in the motivic context and its connection to the nearby cycles derived from motivic integration.

Hình thức: Online qua google meet, cụ thể https://meet.google.com/yep-kbzk-eao?pli=1&authuser=1