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ax–schanuel conjecture

Journal of the Institute of Mathematics of Jussieu (1)

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AX–SCHANUEL CONDITION IN ARBITRARY CHARACTERISTIC
Part of
- Diophantine approximation, transcendental number theory
- Differential and difference algebra
Piotr Kowalski
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 18 / Issue 6 / November 2019

Published online by Cambridge University Press:

08 November 2017, pp. 1157-1213

Print publication:

November 2019
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We prove a positive characteristic version of Ax’s theorem on the intersection of an algebraic subvariety and an analytic subgroup of an algebraic group [Ax, Some topics in differential algebraic geometry. I. Analytic subgroups of algebraic groups, Amer. J. Math.94 (1972), 1195–1204]. Our result is stated in a more general context of a formal map between an algebraic variety and an algebraic group. We derive transcendence results of Ax–Schanuel type.