Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational points on certain homogeneous varieties   Let $L$ be a simply-connected simple connected algebraic group over a number
field $F$, and $H$ be a semisimple absolutely maximal connected $F$-subgroup of
$L$. Under a cohomological condition, we prove an asymptotic formula for the
number of rational points of bounded height on projective equivariant
compactifications of $\Delta(H)\backslash L^n$ with respect to a balanced line
bundle, where $\Delta(H)$ is the image of $H$ diagonally embedded in $L^n$.

34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs