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AX–SCHANUEL CONDITION IN ARBITRARY CHARACTERISTIC

Part of: Diophantine approximation, transcendental number theory Differential and difference algebra

Published online by Cambridge University Press:  08 November 2017

Piotr Kowalski
Piotr Kowalski*
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland (pkowa@math.uni.wroc.pl)http://www.math.uni.wroc.pl/∼pkowa/
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Abstract

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.

Keywords

Ax–Schanuel conjectureformal mapstranscendence

MSC classification

Primary: 11J91: Transcendence theory of other special functions
Secondary: 12H05: Differential algebra
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 6 , November 2019 , pp. 1157 - 1213
Copyright
© Cambridge University Press 2017 

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Footnotes

Supported by Narodowe Centrum Nauki grants nos. NCN 2012/07/B/ST1/03513, 2015/19/B/ST1/ 01150 and 2015/19/B/ST1/01151; and by ANR Modig (ANR-09-BLAN-0047).

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