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Arithmetic Conjectures and their Special Sets

Connections Workshop: Diophantine Geometry February 02, 2023 - February 03, 2023

February 03, 2023 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Natalia Garcia-Fritz (Pontificia Universidad Catolica de Chile)
Location: MSRI: Simons Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Abstract

It is often the case that in concrete Diophantine problems it is not enough to show that the rational points on a variety are algebraically degenerate; one also needs to describe their Zariski closure. In arithmetic questions such as Vojta's conjecture and the Bombieri-Lang conjecture, this Zariski closure is referred to as the special set. In this talk I will explain some techniques based in omega-integrality to describe the special set in Diophantine conjectures over number fields and function fields, and to prove some instances of these conjectures in the function field case.

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