Symplectic representations of inertia groups
Abstract
Suppose $\ell$ is a prime number, $\ell >3$, $K$ is a field that is an unramified finite extension of the field $\Q_\ell$ of $\ell$adic numbers, and $G$ is a finite group that is a semidirect product of a normal $\ell'$subgroup $H$ and a cyclic $\ell$group $L$. Suppose that the group algebra $K[H]$ is decomposable. If there exists an embedding of $G$ in the symplectic group $\Sp_{2d}(K)$ for some positive integer $d$, then there exists an embedding of $G$ in $\Sp_{2d}({\mathcal O}_K)$, where ${\mathcal O}_K$ is the ring of integers of $K$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2000
 arXiv:
 arXiv:math/0009024
 Bibcode:
 2000math......9024S
 Keywords:

 Number Theory;
 Group Theory;
 11E95;
 11S23;
 20C11;
 20G25
 EPrint:
 LaTeX2e, 7 pages