Ramified primes in the field of definition for the MordellWeil group of an elliptic surface
Author:
Masato Kuwata
Journal:
Proc. Amer. Math. Soc. 116 (1992), 955959
MSC:
Primary 11G35; Secondary 14D10, 14G05, 14J27
MathSciNet review:
1116264
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Abstract: Let be an elliptic surface defined over a number field . We consider the field in which all the sections are defined. Assuming that the invariant is nonconstant, is again a number field. We describe the primes of possible ramification of the extension in terms of the configuration of the points of bad fibers in . Aside from few possible exceptions, is unramified outside of the primes of bad reduction of and the primes for which two or more points of bad fibers become identical modulo .
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 Masato Kuwata, The field of definition of the MordellWeil group of an elliptic curve over a function field, Compositio Math. 76 (1990), 399406. MR 1080009 (91j:11042)
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 , Jacobian varieties, Arithmetic Geometry (G. Cornell and J. H. Silverman, eds.), SpringerVerlag, New York, 1986, pp. 167212. MR 861976
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 Joseph H. Silverman, The arithmetic of elliptic curves, SpringerVerlag, New York, 1986. MR 817210 (87g:11070)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199211162640
PII:
S 00029939(1992)11162640
Keywords:
Elliptic surfaces
Article copyright:
© Copyright 1992
American Mathematical Society
