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- W2043828816 abstract "The field of moduli K of a curve X a priori defined over the separable closure K5 of K need not be a field of definition. This paper shows that the obstruction is essentially the same as the obstruction to K being a field of definition of the cover X → X/Aut(X). Using previous results of Dèbes-Douai, we then obtain a cohomological measure of the obstruction. This yields concrete criteria for the field of moduli to be a field of definition. An interesting application is the following local-global principle. If a curve X, together with all of its automorphisms, is defined over ℚp for all primes p, then it is defined over ℚ." @default.
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- W2043828816 date "1999-01-01" @default.
- W2043828816 modified "2023-10-17" @default.
- W2043828816 title "On fields of moduli of curves" @default.
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- W2043828816 doi "https://doi.org/10.1006/jabr.1998.7586" @default.
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