Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational points in periodic analytic sets and the Manin-Mumford
  conjecture   We present a new proof of the Manin-Mumford conjecture about torsion points
on algebraic subvarieties of abelian varieties. Our principle, which admits
other applications, is to view torsion points as rational points on a complex
torus and then compare (i) upper bounds for the number of rational points on a
transcendental analytic variety (Bombieri-Pila-Wilkie) and (ii) lower bounds
for the degree of a torsion point (Masser), after taking conjugates. In order
to be able to deal with (i), we discuss (Thm. 2.1) the semi-algebraic curves
contained in an analytic variety supposed invariant for translations by a full
lattice, which is a topic with some independent motivation.

16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph