Clay Mathematics Institute

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Positive characteristic version of Ax's theorem

Piotr Kowalski (Wroclaw University)

Abstract:  Ax's theorem on the dimension of the intersection of an algebraic subvariety and a formal subgroup (Theorem 1F in "Some topics in differential algebraic geometry I...") implies Ax-Schanuel type transcendence results for a vast class of formal maps (including the exponential map on a semi-abelian variety). Ax stated and proved this theorem in the case of characteristic 0, but the statement is also meaningful for arbitrary characteristic and still implies Ax-Schanuel type transcendence results. I will discuss my work on characteristic version of Ax's theorem.