Ramified primes in the field of definition for the Mordell-Weil group of an elliptic surface
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- by Masato Kuwata PDF
- Proc. Amer. Math. Soc. 116 (1992), 955-959 Request permission
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 $\mathfrak {p}$.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 955-959
- MSC: Primary 11G35; Secondary 14D10, 14G05, 14J27
- DOI: https://doi.org/10.1090/S0002-9939-1992-1116264-0
- MathSciNet review: 1116264