Premium
Function Fields and Elementary Equivalence
Author(s) -
Pierce David A.
Publication year - 1999
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609398005621
Subject(s) - mathematics , algebraically closed field , function field , endomorphism , isomorphism (crystallography) , pure mathematics , equivalence relation , equivalence (formal languages) , elliptic curve , elementary function , zero (linguistics) , multiplication (music) , algebra over a field , field (mathematics) , mathematical analysis , combinatorics , linguistics , philosophy , chemistry , crystal structure , crystallography
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.