Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heights and arithmetic dynamics over finitely generated fields   We develop a theory of vector-valued heights and intersections defined
relative to finitely generated extensions K/k. These generalize both number
field and geometric heights. When k is Q or F_p, or when a non-isotriviality
condition holds, we obtain Northcott-type results. We then prove a version of
the Hodge Index Theorem for vector-valued intersections, and use it to prove a
rigidity theorem for polarized dynamical systems over any field.

21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn