Ramification of primes in fields of moduli
-- Andrew Obus, October 2, 2009

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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. 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.