Galois Groups of Unramified Covers of Projective Curves in Characteristicp Original Research Article

We show several results concerning the finite groups that occur as Galois groups of unramified covers of projective curves in characteristicp. In particular, we prove that every finite group withimagegenerators occurs over some curve of genusimage. This implies, for example, that every finite simple group occurs in genus 2. By similar methods, we obtain several other families of groups which occur in genus 2. In addition, we show that if a groupGoccurs over some curve of genusimage, then it must occur over “almost all” curves of genusimageor greater. The results are obtained using formal patching.