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Iskovskikh Seminar
April 26, 2018 18:00, Moscow, Steklov Mathematical Institute, room 540

Specialization of a birational equivalence

A. I. Efimov

Abstract: We will explain the proof of the following theorem of Kontsevich and Tschinkel. Let $X\to B$ and $X'\to B$ be smooth and proper morphisms to a smooth connected curve $B$ over a field of characteristic zero. Suppose that their fibers over the generic point are birational (over the function field of $B$). Then their fibers over any closed point $b\in B$ are birational (over the residue field at $b$).