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A note on extensions of algebraic and formal gorups I.

Noriyuki Suwa, Tsutomu Sekiguchi (1991)

Mathematische Zeitschrift

A note on extensions of algebraic and formal groups II.

Noriyuki Suwa, Tsutomu Sekiguchi (1994)

Mathematische Zeitschrift

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...