The Geometry and Arithmetic of Elliptic Surfaces

Details The Geometry and Arithmetic of Elliptic Surfaces The Geometry and Arithmetic of Elliptic Surfaces

1992-02-14

arxiv.org/abs/alg-geom/9202011v1

Mathematics

Algebraic Geometry

12 pages, Plain TeX

Scientific paper

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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