Báo cáo viên: Ning Guo (Harbin Institute of Technology)
Thời gian: 16h30 Thứ Năm ngày 20/02/2025
Địa điểm: Báo cáo thực hiện trực tiếp tại: Phòng 612 nhà A6 - Viện Toán học
và Online (Join Zoom Meeting) tại link: https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1
Tóm tắt: Various problems concerning cohomology sets and K-theory, including Gersten's injectivity and the Grothendieck-Serre conjecture, have affirmative answers in the equi-characteristic case. A helpful tool for dealing with mixed characteristic cases is geometric presentation theorems. Roughly speaking, these theorems realize the local ring under consideration as a relatively smooth (or étale) object over a regular DVR or a field with a low relative dimension such that problems reduce to the DVR or field cases. In this talk, we will discuss several geometric presentation theorems (due to Gabber-Quillen, Colliot-Thélène, Ojanguren, etc) and see their application to the Grothendieck-Serre conjecture in the mixed characteristic case. In particular, I will introduce the notion of weak elementary fibrations, which traces back to Artin's "bon voisinage" in SGA4. These are individual joint works with Ivan Panin, Fei Liu and Yisheng Tian. |
