The Geometry and Arithmetic of Elliptic Surfaces

zbMATH Open0785.14013arXivalg-geom/9202011MaRDI QIDQ4035817

Peter F. Stiller

Publication date: 18 May 1993

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.

Full work available at URL: https://arxiv.org/abs/alg-geom/9202011

zbMATH Keywords

Mordell-Weil rankelliptic curvePicard numberelliptic surfaces

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves (14H52) Elliptic surfaces, elliptic or Calabi-Yau fibrations (14J27)

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