Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on Frobenius divided modules in mixed characteristics   If $X$ is a smooth scheme over a perfect field of characteristic $p$, and if
$\sD_X$ is the sheaf of differential operators on $X$ [EGAIV], it is well known
that giving an action of $\sD_X$ on an $\sO_X$-module $\sE$ is equivalent to
giving an infinite sequence of $\sO_X$-modules descending $\sE$ via the
iterates of the Frobenius endomorphism of $X$. 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 formal schemes such that $p$ belongs to an ideal of definition.
In a recent preprint, dos Santos used this result to lift $\sD_X$-modules from
characteristic $p$ to characteristic 0 with control of the differential Galois
group.

16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph