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A conjecture in the arithmetic theory of differential equations

Nicholas M. Katz (1982)

Bulletin de la Société Mathématique de France

A generalization of the method of global relation.

Chirskiĭ, V.G. (2005)

Journal of Mathematical Sciences (New York)

A generalization of the sizes of differential equations and its applications to $G$ -function theory

Makoto Nagata (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

A note on Frobenius divided modules in mixed characteristics

Pierre Berthelot (2012)

Bulletin de la Société Mathématique de France

If $X$ is a smooth scheme over a perfect field of characteristic $p$ , and if $𝒟_{X}^{(\infty)}$ is the sheaf of differential operators on $X$ [7], it is well known that giving an action of $𝒟_{X}^{(\infty)}$ on an $𝒪_{X}$ -module $ℰ$ is equivalent to giving an infinite sequence of $𝒪_{X}$ -modules descending $ℰ$ via the iterates of the Frobenius endomorphism of $X$ [5]. We show that this result can be generalized to any infinitesimal deformation $f : X \to S$ of a smooth morphism in characteristic $p$ , endowed with Frobenius liftings. We also show that it extends to adic...

An application of newton iteration procedure to $p$ -adic differential equations

Yasutaka Sibuya (1979/1981)

Groupe de travail d'analyse ultramétrique

An example of an arithmetic Fuchsian group.

Daan Krammer (1995)

Journal für die reine und angewandte Mathematik

$B_{dR}$ -représentations dans le cas relatif

Fabrizio Andreatta, Olivier Brinon (2010)

Annales scientifiques de l'École Normale Supérieure

Dans ce travail nous développons un analogue relatif de la théorie de Sen pour les $B_{dR}$ -représentations. On donne des applications à la théorie des représentations $p$ -adiques, en la reliant à la théorie des $(ϕ, Γ)$ -modules relatifs, et à celle des modules de Higgs $p$ -adiques développée par G. Faltings.