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Fields with finitely many definable subsets

Wednesday 15th June 2005 - 10:30 to 12:00
INI Seminar Room 2

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
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons