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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ramified primes in the field of definition for the Mordell-Weil group of an elliptic surface


Author: Masato Kuwata
Journal: Proc. Amer. Math. Soc. 116 (1992), 955-959
MSC: Primary 11G35; Secondary 14D10, 14G05, 14J27
MathSciNet review: 1116264
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Abstract: Let $ \pi :X \to C$ be an elliptic surface defined over a number field $ k$. We consider the field $ K$ in which all the sections are defined. Assuming that the $ j$-invariant is nonconstant, $ K$ is again a number field. We describe the primes of possible ramification of the extension $ K/k$ in terms of the configuration of the points of bad fibers in $ C$. Aside from few possible exceptions, $ K/k$ is unramified outside of the primes of bad reduction of $ C$ and the primes $ \mathfrak{p}$ for which two or more points of bad fibers become identical modulo $ \mathfrak{p}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1116264-0
PII: S 0002-9939(1992)1116264-0
Keywords: Elliptic surfaces
Article copyright: © Copyright 1992 American Mathematical Society