Vol. 128, No. 1, 1987

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 332: 1  2
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
The Picard numbers of elliptic surfaces with many symmetries

Peter Frederick Stiller

Vol. 128 (1987), No. 1, 157–189
Abstract

In this paper we compute the Picard numbers of several families of elliptic surfaces (see Example 1, §5 for a typical result.) This is equivalent to the difficult problem of determining the rank of the Mordell-Weil group of certain elliptic curves over function fields. Our method is to study the action induced by automorphisms of these surfaces on a relevant part of the cohomology. The cohomology classes are represented by certain inhomogeneous differential equations—our so-called inhomogeneous de Rham cohomology—where the effect of the action is easily understood.

Mathematical Subject Classification 2000
Primary: 14J27
Secondary: 11G99, 14C30, 14J05
Milestones
Received: 28 August 1985
Revised: 30 April 1986
Published: 1 May 1987
Authors
Peter Frederick Stiller