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Seminar

DDC - Diophantine Problems: Diophantine problems over large fields October 19, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program:
Location: SLMath: Online/Virtual
Speaker(s) Arno Fehm (TU Dresden)
Description

This seminar will focus on Diophantine problems in a broad sense, with a view towards (but not limited to) interactions between Number Theory and Logic. Particular attention will be given to topics with the potential of further developments in the context of this MSRI scientific program. This will provide an opportunity for researchers to update on new results, techniques and some of the main problems of the field.

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

Diophantine Problems Over Large Fields

Abstract/Media

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

Abstract:

A field K is large if every smooth K-curve with a K-rational point has infinitely many of these. Large fields were introduced in the context of Galois theory, where they now play an important role, but they happen to show up naturally also in several other areas, such as valuation theory, arithmetic geometry and model theory. In this talk I will give a brief introduction to large fields, will survey some results regarding diophantine sets involving large fields, and will then explain in more detail why over a large field one usually cannot find an abelian variety of finite Mordell-Weil rank, a fact (obtained in joint work with S. Petersen) that is relevant in the context of Hilbert's tenth problem.

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Diophantine Problems Over Large Fields

H.264 Video 25172_28670_8578_Diophantine_Problems_Over_Large_Fields.mp4