Representations associated with elliptic surfaces

David Cox and Walter Raymond Parry

Vol. 114 (1984), No. 2, 309–323

DOI: 10.2140/pjm.1984.114.309

Abstract

An elliptic surface (over C) f : X → S with a section has two representations naturally associated to it: the first, the monodromy representation, is determined by the topology of f, while the second, the Galois representation, is determined by the arithmetic of the general fiber of f. The purpose of this paper is to study and compare the properties of these representations.

Mathematical Subject Classification 2000

Primary: 14K15

Secondary: 11G05, 14D05, 14J27

Milestones

Received: 3 September 1982

Published: 1 October 1984