Realization conjecture for finite groups as Galois groups of coverings
Realization conjecture for finite groups as Galois groups of coverings
Let be the function field of the projective line, and let be a finite regular Galois extension of with Galois group . Equivalently, the inclusion defines a ramified Galois covering over with Galois group . Realization conjecture. Every finite group occurs as the Galois group of such a covering. This is a realization problem for finite groups as Galois groups of regular function-field extensions, and the supplied text does not state whether the claim is known or open.
Sources & referencesView supporting material
Primary source
Alberto Besana and Cristina Martinez, “Enumerative geometry of the curves defined by y^d=f(x)”, arXiv:1111.6456 (2012).
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