Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Canonical heights and the arithmetic complexity of morphisms on
  projective space   Let F and G be morphisms of degree at least 2 from P^N to P^N that are
defined over the algebraic closure of Q. We define the arithmetic distance
d(F,G) between F and G to be the supremum over all algebraic points P of
|h_F(P)-h_G(P)|, where h_F and h_G are the canonical heights associated to the
morphisms F and G, respectively. We prove comparison theorems relating d(F,G)
to more naive height functions and show that for a fixed G, the set of F
satisfying d(F,G) < B is a set of bounded height. In particular, there are only
finitely many such F defined over any given number field.

9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int