Explicit 8-descent on elliptic curves

  • In this thesis I describe an explicit method for performing an 8-descent on an elliptic curve E over the rational numbers. An 8-descent is the next step after a 2- and a 4-descent. The method of 2-descent belongs to the classical tools in arithmetic geometry. More recent is the exploration of higher 2-descent. In 1996 Merriman, Siksek, and Smart found a method for doing 4-descent, and a different method for 4-descent was presented in 1998 by Cassels. I have been working on extending these methods to an 8-descent. I present a method for computing the 8-Selmer group of E as an abstract group, and next, for representing its elements as 8-coverings of E. With this method I was able to compute some examples, one of which is a curve of order 8 in the Shafarevich-Tate group of an elliptic curve. This is the first explicit example of a curve of such high order in Sha.

Download full text

Cite this publication

  • Export Bibtex
  • Export RIS

Citable URL (?):

Search for this publication

Search Google Scholar Search Catalog of German National Library Search OCLC WorldCat Search Catalog of GBV Common Library Network Search Catalog of Jacobs University Library Search Bielefeld Academic Search Engine
Meta data
Publishing Institution:IRC-Library, Information Resource Center der Jacobs University Bremen
Granting Institution:Internat. Univ.
Author:Sebastian Karl Michael Stamminger
Referee:Michael Stoll, Dierk Schleicher, John E. Cremona
Advisor:Michael Stoll
Persistent Identifier (URN):urn:nbn:de:101:1-201305171186
Document Type:PhD Thesis
Language:English
Date of Successful Oral Defense:2005/12/09
Year of First Publication:2005
PhD Degree:Mathematics
Library of Congress Classification:Q Science / QA Mathematics (incl. computer science)
School:SES School of Engineering and Science
Call No:Thesis 2005/10

$Rev: 13581 $