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Multiplication complexe et équivalence élémentaire dans le langage des corps (Complex multiplication and elementary equivalence in the language of fields)

Published online by Cambridge University Press:  12 March 2014

Xavier Vidaux
Xavier Vidaux*
Affiliation:
Département de Mathématiques, Université du Maine, Avenue Olivier Messiaen, 72085 le Mans Cedex 9, France, E-mail: Xavier.Vidaux@univ-lemans.fr
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Abstract

Let K and K′ be two elliptic fields with complex multiplication over an algebraically closed field k of characteristic 0. non k-isomorphic, and let C and C′ be two curves with respectively K and K′ as function fields. We prove that if the endomorphism rings of the curves are not isomorphic then K and K′ are not elementarily equivalent in the language of fields expanded with a constant symbol (the modular invariant). This theorem is an analogue of a theorem from David A. Pierce in the language of k-algebras.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 2 , June 2002 , pp. 635 - 648
Copyright
Copyright © Association for Symbolic Logic 2002

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References

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