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Computational arithmetic geometry : AMS Special Session, April 29-30, 2006, San Francisco State University, San Francisco, California / Kristin E. Lauter, Kenneth A. Ribet, editors.
- Format:
- Book
- Conference/Event
- Author/Creator:
- AMS Special Session on Computational Arithmetic Geometry, Corporate Author.
- Conference Name:
- AMS Special Session on Computational Arithmetic Geometry (2006 : San Francisco, Calif.), issuing body.
- AMS Special Session on Computational Arithmetic Geometry
- Series:
- Contemporary mathematics (American Mathematical Society). 0271-4132 463
- Contemporary mathematics, 463 0271-4132
- Language:
- English
- Subjects (All):
- Arithmetical algebraic geometry--Congresses.
- Arithmetical algebraic geometry.
- Algebraic number theory--Congresses.
- Algebraic number theory.
- Physical Description:
- 1 online resource (146 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2008]
- Language Note:
- English
- Summary:
- With the recent increase in available computing power, new computations are possible in many areas of arithmetic geometry. To name just a few examples, Cremona's tables of elliptic curves now go up to conductor 120,000 instead of just conductor 1,000, tables of Hilbert class fields are known for discriminant up to at least 5,000, and special values of Hilbert and Siegel modular forms can be calculated to extremely high precision. In many cases, these experimental capabilities haveled to new observations and ideas for progress in the field. They have also led to natural algorithmic questions on the feasibility and efficiency of many computations, especially for the purpose of applications in cryptography. The AMS Special Session on Computational Arithmetic Geometry, held onApril 29-30, 2006, in San Francisco, CA, gathered together many of the people currently working on the computational and algorithmic aspects of arithmetic geometry. This volume contains research articles related to talks given at the session. The majority of articles are devoted to various aspects of arithmetic geometry, mainly with a computational approach.
- Contents:
- Contents
- Preface
- Schedule of talks
- Results of Cohen-Lenstra type for quadratic function fields
- The hardness of computing an eigenform
- Constructing elliptic curves of prime order
- Space-time codes and non-associative division algebras arising from elliptic curves
- Points of low height on P1 over number fields and bounds for torsion in class groups
- Supersingular genus-2 curves over fields of characteristic 3
- Search techniques for root-unitary polynomials
- Yet more elements in the Shafarevich-Tate group of the Jacobian of a Fermat Curve
- Stable reduction of X0(81)
- Isomorphism types of commutative algebras of finite rank over an algebraically closed field
- A short guide to p-torsion of abelian varieties in characteristic p.
- Notes:
- Description based upon print version of record.
- Description based on print version record.
- ISBN:
- 0-8218-8142-6
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