The Geometry and Arithmetic of Elliptic Surfaces

1992/02/14 by Peter F. Stiller, Stiller, Peter F.
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.alg-geom/9202011

openalex publication_date 1992/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Elliptic Surfaces
• Geometric and arithmetic aspects of rational elliptic surfaces
• Determining explicitly the Mordell-Weil group of certain rational elliptic surfaces
• The Maximal Rank of Elliptic Delsarte Surfaces
• Noncommutative geometry of elliptic surfaces