The Geometry and Arithmetic of Elliptic Surfaces
alg-geom
2008-02-03 v1 Algebraic Geometry
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.
Cite
@article{arxiv.alg-geom/9202011,
title = {The Geometry and Arithmetic of Elliptic Surfaces},
author = {Peter F. Stiller},
journal= {arXiv preprint arXiv:alg-geom/9202011},
year = {2008}
}
Comments
12 pages, Plain TeX