Mathematical Sciences Research Institute

Home » Workshop » Schedules » Arithmetic Conjectures and their Special Sets

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
No Video Uploaded

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.

Supplements No Notes/Supplements Uploaded
Video/Audio Files
No Video Files Uploaded