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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.

University of Cambridge Research Councils UK
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