Time：15:00-16:00, Thursday, September 26 2024
Venue：E4-233
Speaker：Ning Guo, Harbin Institute of Technology
Title：Geometric presentation theorems and applications
Abstract：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 and Fei Liu.
