时间：2024年9月26日（星期四）15:00-16:00
地点：西湖大学云谷校区E4-233
主讲人：哈尔滨工业大学 郭宁
报告题目：Geometric presentation theorems and applications
报告摘要：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.
