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

2011/08/08 by Francesco Baldassarri, Baldassarri, Francesco · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.NT

paper · pdf · doi:10.48550/arxiv.1108.1633

This paper has been withdrawn because a new version with a new title is going to be posted

openalex publication_date 2011/08/08 · arxiv created 2012/09/01 · arxiv updated 2012/09/04 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We illustrate the theory of the radius of convergence of a connection on a p-adic curve X, by deducing from it a simple proof of a variant of Alain Robert's p-adic Rolle theorem. We need to carefully compare our global notion of radius of convergence, depending on the choice of a semistable formal model of X, and the local intrinsic notion of radius of convergence at a point x of Berkovich type 2 or 3, of Kedlaya. (Both notions go back to Dwork, Robba, Christol,...). The coincidence of the two notions when x is a point of the skeleton of the chosen semistable formal model of X, is crucial in the conclusion of our proof. The same method applies to the discussion of the p-adic geometric ramification locus, in the sense of Berkovich, of an etale covering of smooth p-adic curves.

Cited by

• Appendix: proof of the Uniformity Conjecture
• Radius of convergence of p-adic connections and the Berkovich ramification locus

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