# Algebraic Geometry and Number Theory with Magma

Institute Henri Poincaré
Paris
October 4 - 8, 2004
# Pictures

Click here for pictures of the conference
(taken by William Stein and Allan Steel).
## Introduction

A week-long conference on the Computer Algebra system
Magma and its
applications to computational algebraic geometry and number theory was held
October 4 - 8, 2004. The meeting was held at the Centre Emile Borel of the
Institute Henri Poincaré, Paris, as part of the trimester on "Explicit
Methods in Number Theory", organised by Belabas, Cohen, Cremona, Mestre,
Roblot, Zagier.
For further information, mail
John Cannon.

The meeting was built around the following types of activities:

- Lectures describing recent developments in algorithms for algebraic
geometry and arithmetic fields.
- Talks describing significant applications of Magma to algebraic
geometry or number theory.
- Talks discussing potential algorithms or ideas for future directions in
computational methods for algebraic geometry and arithmetic fields.
- Short courses on the use of Magma in following areas:
- Arithmetic fields
- General algebraic geometry ie schemes
- Elliptic curves
- Curves of genus greater than 1
- Modular forms and modular abelian varieties

## Lectures

Manjul Bhargava (IAS Princeton): *A conjecture of Conway and
Schneeberger on quadratic forms*

Gavin Brown (Warwick): *Graded rings over K3 surfaces*

John Cannon (Sydney): *An overview of algebraic geometry in Magma*

John Cremona (Nottingham): *Finding all elliptic curves with good reduction
outside a given set of primes*

Miles Reid (Warwick): *Unprojection and Gorenstein rings in small codimensions*

Josef Schicho (Linz): *Deciding rational rationality of algebraic surfaces*

Frank-Olaf Schreyer (Saarbrücken): *Computation of cohomology of coherent
sheaves*

Allan Steel (Sydney): *Computing Gröbner bases using linear
algebra*

William Stein (Harvard): *Computations related to the BSD conjecture for
modular abelian varieties using MAGMA*

Jan Stevens (Goeteborg): *Computing in singularity theory*

Michael Stoll (IU, Bremen): *Implementing the Brauer-Manin obstruction on curves*

## Short Courses

A number of short courses providing an introduction to the use of Magma in
various branches of algebraic geometry and number theory will be presented. The
lectures, in most cases, will be presented by people who have played a major
role in the development of the corresponding machinery in Magma. Each course
will comprise two one hour lectures. Some talks in the list below have still
to be confirmed.
#### Arithmetic Fields

W Bosma (Nijmegen): *Number fields*

F Hess (TU, Berlin): *Algorithms for function fields and curves with
applications in cryptography and coding theory*

#### Algebraic Geometry

G Brown (Warwick): *Schemes*

M Harrison (Sydney): *Maps between schemes*

#### Elliptic Curves

J Cremona (Nottingham): *Elliptic curves over general fields*

J Cremona (Nottingham): *Elliptic curves over number fields*

#### Curves of Genus Greater than One

M Stoll (IU, Bremen): *Hyperelliptic curves and curves of genus 2*

M Stoll (IU, Bremen): *General curves*

#### Modular Forms

W Stein (Harvard): *Modular symbols and modular forms*

W Stein (Harvard): *Modular abelian varieties*

### Organisers

John Cannon

Gavin Brown

Claus Fieker

*Last modified on 26 August 2004 by
claus@maths.usyd.edu.au*