Radius of convergence of p-adic connections and the Berkovich ramification locus

2012/09/01 by Francesco Baldassarri, Baldassarri, Francesco
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1209.0081

new version of arXiv:1108.1633v3. Michael Temkin informed us of a substantial error in the previous version of this paper. This is now corrected and the structure of the paper is very much simplified

openalex publication_date 2012/09/01 · arxiv created 2012/12/23 · arxiv updated 2012/12/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We apply the theory of the radius of convergence of a p-adic connection to the special case of the direct image of the constant connection via a finite morphism of compact p-adic curves, smooth in the sense of rigid geometry. In the case of an etale covering of curves with good reduction, we get a lower bound for that radius and obtain a new geometric proof of a variant of the p-adic Rolle theorem of Robert and Berkovich. We take this opportunity to clarify the relation between our notion of radius of convergencand the more intrinsic one used by Kedlaya

Citations

• Radius of convergence of p-adic connections: an application to the p-adic Rolle theorem

Related

• Radius of convergence of p-adic connections: an application to the p-adic Rolle theorem
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• Continuity of the radius of convergence of p-adic differential equations on Berkovich analytic spaces