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Non-archimedean Yomdin-Gromov parametrizations and points of bounded height

Model Theory in Geometry and Arithmetic May 12, 2014 - May 16, 2014

May 13, 2014 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): François Loeser (Université de Paris VI (Pierre et Marie Curie))
Location: MSRI: Simons Auditorium
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Abstract

We shall discuss versions of the Yomdin-Gromov reparametrization lemma valid in a non-archimedean setting. Special care is needed in order to insure these parametrizations are globally well approximated by their Taylor expansions. We shall present as applications a $p$-adic version of the Pila-Wilkie theorem and a geometric analogue of estimates of Bombieri-Pila and Pila for the number of integral points of bounded height on affine algebraic varieties. This is joint work with R. Cluckers and G. Comte. 

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