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Seminar

Curve-Excluding Fields August 09, 2022 (02:15 PM PDT - 03:00 PM PDT)
Parent Program:
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Speaker(s) Jinhe Ye (Institut de Mathématiques de Jussieu)
Description No Description
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Curve-Excluding Fields
Abstract/Media

Consider the class of fields with Char$(K)=0$ such that $x^4+y^4=1$ has only 4 solutions in $K$. We show that it has a model companion, curve-excluding fields. Curve-excluding fields provide examples to various questions. Model-theoretically, they are model complete and algebraically bounded. Field-theoretically, they can be non-large when we vary the curve of choice.  Moreover, there exist decidable curve-excluding fields. This is based on joint work with Will Johnson and Erik Walsberg.

93866?type=thumb Curve-Excluding Fields 310 KB application/pdf

Curve-Excluding Fields