Seminar
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| Location: | SLMath: Online/Virtual |
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
Diophantine Problems Over Large Fields
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.
No Notes/Supplements UploadedDiophantine Problems Over Large Fields
| H.264 Video | 25172_28670_8578_Diophantine_Problems_Over_Large_Fields.mp4 |