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Dwork’s conjecture on the logarithmic growth of solutions of p-adic differential equations

Part of: Differential and difference algebra

Published online by Cambridge University Press:  01 March 2008

Yves André
Yves André*
Affiliation:
Département de Mathématiques et Applications, École Normale Supérieure, 45 rue d’Ulm, 75230 Paris cedex 05, France (email: andre@dma.ens.fr)
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Abstract

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This is a study of the asymptotic behaviour of solutions of p-adic linear differential equations near the boundary of their convergence disks. We prove Dwork’s conjecture on the logarithmic growth of solutions in generic versus special disks.

Keywords

p-adic differential equationslogarithmic growthNewton polygonsspecializationsemi-continuity

MSC classification

Secondary: 12H25: $p$-adic differential equations
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 2 , March 2008 , pp. 484 - 494
Copyright
Copyright © Foundation Compositio Mathematica 2008