Conditions related to \(\pi_1\) of projective curves
Let \(D\) be a curve of genus \(g\) over an algebraically closed field of positive characteristic \(p\). We write \(\pi_A(D)\) for the set of isomorphism classes of of finite groups occurring as Galois groups of unramified covers of \(D\). This paper is concerned with giving necessary and sufficient conditions for a family of groups to lie in \(\pi_A(D)\). The main tool is a criterion of Nakajima concerning generators of group rings. The author first reviews the known results and gives a comparison between some necessary conditions. In particular, she shows that for many groups, Nakajima's criterion does not follow from previously known criteria. Then the author goes on to consider a specific class of groups for which she shows that Nakajima's condition is not only necessary but also sufficient. In the last section more specific results about tame covers of genus two curves are derived.
scientific article; zbMATH DE number 1207953