Diameter-Extremal Subsets of Spheres.
Let be a field of characteristic , a proper, smooth, geometrically connected curve over , and 0 and two -rational points on . We show that any representation of the local Galois group at extends to a representation of the fundamental group of which is tamely ramified at 0, provided either that is separately closed or that is . In the latter case, we show there exists a unique such extension, called “canonical”, with the property that the image of the geometric fundamental group...
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