Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unlikely intersections on the $p$-adic formal ball   We prove a $p$-adic formal version of the Mordell-Lang conjecture in the
multiplicative case, characterizing subschemes of a formal torus
$\hat{\mathbb{G}}_m^n$ which have dense intersection with the divisible hull of
certain finitely generated subgroups. This sheds some light on when $p$-adic
deformations interpolate Zariski-dense sets of automorphic objects. In
particular, we show that a component of the closure in weight space of a set of
locally algebraic weights is the translate of a formal torus. We then outline
some consequences for the nearly ordinary $p$-adic families of cuspidal
cohomological automorphic forms for the general linear group constructed by
Hida.

26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th