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A remark on the moduli field of a curve

✍ Scribed by H. Hammer; F. Herrlich


Publisher
Springer
Year
2003
Tongue
English
Weight
86 KB
Volume
81
Category
Article
ISSN
0003-889X

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The field of moduli K of a curve X a priori defined over the separable closure K s 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 Dbbes-Doua

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## Abstract In this paper we study the Newton polygon of the __L__ ‐polynomial __L__ (__t__) associate to the Picard curves __y__^3^ = __x__^4^ – 1, __y__^3^ = __x__^4^ – __x__ defined over a finite field 𝔽~__p__~ . In the former case we get a complete classification. In the latter case we obtai