English

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.

Keywords

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

R2 v1 2026-07-22T07:41:02.174Z