Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the arithmetic self-intersection number of the dualizing sheaf on
  arithmetic surfaces   We study the arithmetic self-intersection number of the dualizing sheaf on
arithmetic surfaces with respect to morphisms of a particular kind. We obtain
upper bounds for the arithmetic self-intersection number of the dualizing sheaf
on minimal regular models of the modular curves associated with congruence
subgroups $\Gamma_0(N)$ with square free level, as well as for the modular
curves X(N) and the Fermat curves with prime exponent.

12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ