Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Approximation of Local Antiderivatives of Relative Differential on
  Arithmetic Surface   Let $\omega$ be a relative differential on aithmetic surface $X$. We
construct a family of rational functions $G_x$ on $X\otimes\Bbb{C}$, which can
approximate local antiderivatives of $\omega$ over an open set on
$X\otimes\Bbb{C}$. From this family of functions, we construct a rational
function $G_2$ on $X$. The function $G_2$ can generate an element in the ring
of integers of a number field, which can approximate an inner product produced
by $\omega$ and the conjugate of $\omega$ over an open set on
$X\otimes\Bbb{C}$. This will give a relation between the height of a rational
curve $E_P$ on $X$ and the canonical norm of $\omega$ on $X\otimes\Bbb{C}$.
This relation will give an upper bound for the height of $E_P$ under a few
assumptions.

9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio