Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-stable models of modular Curves $X_0(p^2)$ and some arithmetic
  applications   In this paper, we compute the semi-stable models of modular curves $X_0(p^2)$
for odd primes $p > 3$ and compute the Arakelov self-intersection numbers of
the relative dualising sheaves for these models. We give two arithmetic
applications of our computations. In particular, we give an effective version
of the Bogomolov conjecture following the strategy outlined by Zhang and find
the stable Faltings heights of the arithmetic surfaces corresponding to these
modular curves.

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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ