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Oberseminar SoSe 2010 Zusammenfassung des Vortrags von A. Obus (Columbia, USA)

Ramification in Fields of Moduli

If G is a finite group, then the field of moduli of a branched G -cover of the Riemann sphere is the intersection of all fields of definition of the G -cover. A result of Beckmann says that for any 3-point G -Galois cover of the Riemann sphere, if a prime p does not divide the order of G, then p is unramified in the field of moduli of the G -cover. Stefan Wewers generalized this: if p exactly divides the order of G, then p is tamely ramified in the field of moduli. We will discuss extensions of this result, contained in the speaker's thesis, involving more general groups G with cyclic p -Sylow groups.