Automorphism groups of curves in characteristic $p>0$
Claus Lehr
Abstract: Together with Michel Matignon we have are studying
automorphism groups of curves in positive characteristic $p$.
One main result of this work is a theorem classifying the $p$-Sylow
subgroups
of the automorphism groups of Artin-Schreier covers of the affine line.
This result is the starting point to understand curves with 'big $p$-group
actions'. For this let $(X,G)$ be a $k$-curve together with a $p$-group
$G$
of automorphisms acting on $X$. We say that $(X,G)$ satisfies the Nakajima
condition (N) if the genus $g_X > 0$ and $|G|/g_X > 2p/(p-1)$.
This condition says that the size of $G$ is big with respect to the genus
of
the curve. We have first results concerning this big actions.