Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the group of purely inseparable points of an abelian variety defined
  over a function field of positive characteristic   Let $K$ be the function field of a smooth and proper curve $S$ over an
algebraically closed field $k$ of characteristic $p>0$. Let $A$ be an ordinary
abelian variety over $K$. Suppose that the N\'eron model $\CA$ of $A$ over $S$
has a closed fibre $\CA_s$, which is an abelian variety of $p$-rank 0. We show
that under these assumptions the group $A(K^\perf)/\Tr_{K|k}(A)(k)$ is finitely
generated. Here $K^\perf=K^{p^{-\infty}}$ is the maximal purely inseparable
extension of $K$. This result implies that in some circumstances, the "full"
Mordell-Lang conjecture, as well as a conjecture of Esnault and Langer, are
verified.

18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys