Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arithmetic height functions over finitely generated fields   In this paper, we propose a new height function for a variety defined over a
finitely generated field over Q. For this height function, we will prove
Northcott's theorem and Bogomolov's conjecture, so that we can recover the
original Raynaud's theorem (Manin-Mumford's conjecture).

34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org