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arXiv · alg-geom/9202011

The Geometry and Arithmetic of Elliptic Surfaces

Peter F. Stiller
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Abstract

We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be equivalent to determining the Mordell-Weil rank of an elliptic curve defined over a function field in one variable. An interesting conjecture concerning Galois actions on the relative de~Rham cohomology of these surfaces is discussed.

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Peter F. Stiller. 1992-02-14. The Geometry and Arithmetic of Elliptic Surfaces. https://arxiv.org/abs/alg-geom/9202011

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