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Fields with finitely many definable subsets

Poonen, B (Berkeley)
Wednesday 15 June 2005, 10:30-12:00

Seminar Room 2, Newton Institute Gatehouse


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.

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