Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Height bounds and the Siegel property   Let $G$ be a reductive group defined over $\mathbb{Q}$ and let $\mathfrak{S}$
be a Siegel set in $G(\mathbb{R})$. The Siegel property tells us that there are
only finitely many $\gamma \in G(\mathbb{Q})$ of bounded determinant and
denominator for which the translate $\gamma.\mathfrak{S}$ intersects
$\mathfrak{S}$. We prove a bound for the height of these $\gamma$ which is
polynomial with respect to the determinant and denominator. The bound
generalises a result of Habegger and Pila dealing with the case of $GL_2$, and
has applications to the Zilber-Pink conjecture on unlikely intersections in
Shimura varieties.
  In addition we prove that if $H$ is a subset of $G$, then every Siegel set
for $H$ is contained in a finite union of $G(\mathbb{Q})$-translates of a
Siegel set for $G$.

11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th