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Seminar

DDC - Definability seminar: Defining subrings using Kato principles October 14, 2020 (10:00 AM PDT - 11:00 AM PDT)
Parent Program:
Location: SLMath: Online/Virtual
Speaker(s) Philip Dittmann (TU Dresden)
Description

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

Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Defining Subrings Using Kato Principles

Abstract/Media

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

Abstract:

Quadratic forms have been used to great effect for definability results, already in J. Robinson's definition of Z in Q. Over global fields, much of their utility comes from the Hasse-Minkowski Theorem and quadratic reciprocity. I will discuss higher-dimensional generalisations of these foundational properties due to Kato, and how these lead to definability results for subrings in finitely generated fields in joint work with F. Pop (the crucial step towards the positive solution to the Elementary Equivalence versus Isomorphism Problem for these fields), and universal definability of subalgebras in one-variable function fields over local or global fields in joint work with N. Daans (inspired by Koenigsmann's universal definition of Z in Q).

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Defining Subrings Using Kato Principles

H.264 Video 25230_28780_8567_Defining_Subrings_Using_Kato_Principles.mp4