FUNCTION FIELDS AND ELEMENTARY EQUIVALENCE

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...

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Bibliographic Details
Published inThe Bulletin of the London Mathematical Society Vol. 31; no. 4; pp. 431 - 440
Main Author PIERCE, DAVID A.
Format Journal Article
LanguageEnglish
Published Cambridge University Press 01.07.1999
Oxford University Press
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ISSN0024-6093
1469-2120
DOI10.1112/S0024609398005621

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Summary: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. 1991 Mathematics Subject Classification 14H52, 11U09, 03C52.
Bibliography:ArticleID:31.4.431
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ISSN:0024-6093
1469-2120
DOI:10.1112/S0024609398005621