# Fields with finitely many definable subsets

Presented by:
B Poonen [Berkeley]
Date:
Wednesday 15th June 2005 -
10:30 to 12:00
Venue:
INI Seminar Room 2
Abstract:

We prove that a field with finitely many definable subsets is finite. We also conjecture a relative version of this statement: If K is a field extension of k, and the collection of sets obtained by intersecting each k-definable subset of K with K-k is finite, then k and K are either both finite or both algebraically closed. This is joint work with Kiran Kedlaya.