This article is about a conjecture in the following area in/related to group theory: algebraic geometry. View all conjectures and open problems
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A finite group , a prime number , a nonsingular projective curve , defined over a field of characteristic . (where ) are points of . Let denote the genus of .
Let denote the subgroup generated by all the -Sylow subgroups of . Then, the following are equivalent:
- occurs as the Galois group of a branched covering of , branched only at the points
- The quotient group has generators.
Progress towards the conjecture
Raynaud settled the conjecture in the affine case, and Harbater proved the full conjecture by building upon this special solution.