Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions of algebraic groups with finite quotient and nonabelian
  2-cohomology   For a finite smooth algebraic group $F$ over a field $k$ and a smooth
algebraic group $\bar G$ over the separable closure of $k$, we define the
notion of $F$-kernel in $\bar G$ and we associate to it a set of nonabelian
2-cohomology. We use this to study extensions of $F$ by an arbitrary smooth
$k$-group $G$. We show in particular that any such extension comes from an
extension of finite $k$-groups when $k$ is perfect and we give explicit bounds
on the order of these finite groups when $G$ is linear. We prove moreover some
finiteness results on these sets.

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin