Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heights and quantitative arithmetic on stacky curves   In this paper we investigate a family of algebraic stacks, the so-called
stacky curves, in the context of the general theory of heights on algebraic
stacks due to Ellenberg, Satriano, and Zureick-Brown. We first give an
elementary construction of a height which is seen to be dual to theirs. Next we
count rational points having bounded E-S-ZB height on a particular stacky
curve, answering a question of Ellenberg, Satriano, and Zureick-Brown. We then
show that when the Euler characteristic of stacky curves is non-positive, that
the E-S-ZB height coming from the anti-canonical divisor class fails to have
the Northcott property. Next we prove a generalized version of a conjecture of
Vojta, applied to stacky curves with negative Euler characteristic and coarse
space $\mathbb{P}^1$, is equivalent to the $abc$-conjecture. Finally, we prove
that in the negative characteristic case the purely "stacky" part of the E-S-ZB
height exhibits the Northcott property.

31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ