Extremal rational elliptic surfaces in characteristic \(p\). I: Beauville surfaces (Q1177424)

\textit{R. Miranda} and \textit{U. Persson} classified all rational elliptic surfaces with sections over the complex numbers such that the Mordell- Weil group of the generic fibre is finite. According to them, these surfaces are called extremal rational elliptic surfaces. Previous results were obtained by \textit{A. Beauville} in the case when all singular fibers are semi-stable. In the paper under review, the author begins the program of classifying extremal rational elliptic surfaces in characteristic \(p\) by classifying all those where the singular fibers are semi-stable. Then the surfaces treated in this paper are the characteristic \(p\) analogues of the surfaces studied by A. Beauville.