Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal bases for direct images of $p$-adic differential modules over
  discs   Let $(k,|\cdot|)$ be a complete and algebraically closed valued field
extension of $(\mathbb{Q}_p,|\cdot|_p)$. Given a finite morphism
$\varphi:\mathscr{D}_1\to \mathscr{D}_2$ of unit discs over $k$, a differential
module $(M,D)$ on $\mathscr{D}_1$ and a point $b\in \mathscr{D}_2(k)$, we
construct explicitly an optimal basis of space of horizontal elements for the
direct image $\varphi_*(M,D)$ at $b$ in terms of the suitable chosen optimal
bases of $(M,D)$ at preimages of $b$ by $\varphi$ and ramification properties
of the morphism.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph