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Home » DDC - Valuation Theory: The étale open topology

Seminar

DDC - Valuation Theory: The étale open topology September 02, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Jinhe Ye (University of Notre Dame)
Description

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Video

The Étale Open Topology

Abstract/Media

For any field K, we introduce natural topologies on K-points of varieties over K, which is defined to be the weakest topology such that étale morphisms are open. This topology turns out to be natural in a lot of settings. For example, when K is algebraically closed, it is easy to see that we have the Zariski topology, and it picks up the valuation topology in many henselian valued fields. Moreover, many topological properties correspond to the algebraic properties of the field. As an application, we will show that large stable fields are separably closed. Joint work with Will Johnson, Chieu-Minh Tran, and Erik Walsberg

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

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The Étale Open Topology

H.264 Video 25214_28728_8469_The_Etale_Open_Topology.mp4