Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ample canonical heights for endomorphisms on projective varieties   We define an "ample canonical height" for an endomorphism on a projective
variety, which is essentially a generalization of the canonical heights for
polarized endomorphisms introduced by Call--Silverman. We formulate a dynamical
analogue of the Northcott finiteness theorem for ample canonical heights as a
conjecture, and prove it for endomorphisms on varieties of small Picard
numbers, abelian varieties, and surfaces. As applications, for the
endomorphisms which satisfy the conjecture, we show the non-density of the set
of preperiodic points over a fixed number field, and obtain a dynamical
Mordell--Lang type result on the intersection of two Zariski dense orbits of
two endomorphisms on a common variety.

1
The categories of this paper are: cs
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg