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FUNCTION FIELDS AND ELEMENTARY EQUIVALENCE

Published online by Cambridge University Press:  01 July 1999

DAVID A. PIERCE
DAVID A. PIERCE
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
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Abstract

Continuing work of Duret, we treat the relation between isomorphism and elementary equivalence of function fields over algebraically closed fields. For function fields of curves, these are ‘usually’ the same, but in characteristic zero, for elliptic curves with complex multiplication, a weak variant of elementary equivalence of their function fields corresponds to isomorphism of the endomorphism rings of the curves, not to isomorphism of the curves themselves.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 4 , July 1999 , pp. 431 - 440
Copyright
© The London Mathematical Society 1999

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