Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On integral points on isotrivial elliptic curves over function field   Let $k$ be a finite field and $L$ be the function field of a curve $C/k$ of
genus $g\geq 1$.
  In the first part of this note, we show that the number of separable
$S$-integral points on a constant elliptic curve $E/L$ is bounded solely in
terms of $g$, the size of $S$ and the rank of the Mordell-Weil group $E(L)$.
  In the second part, we assume that $L$ is the function field of a
hyperelliptic curve $C_A:s^2=A(t)$, where $A(t)$ is a square-free
$k$-polynomial of odd degree. If $\infty$ is the place of $L$ associated to the
point at infinity of $C_A$, then we prove that the set of separable
$\{\infty\}$-points can be bounded solely in terms of $g$ and does not seem to
depend on the Mordell-Weil group $E(L)$. This is done by bounding the number of
separable integral points over $k(t)$ on elliptic curves of the form
$E_A:A(t)y^2=f(x)$, where $f(x)$ is a polynomial over $k$. Additionally, we
show that, under an extra condition on $A(t)$, the existence of a separable
integral point of "small" height on the elliptic curve $E_A/k(t)$ determines
the isomorphism class of the elliptic curve $y^2=f(x)$.

15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th