Computational arithmetic geometry : AMS special session, April 29-30, 2006, San Francisco State University, San Francisco, California
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Bibliographic Information
Computational arithmetic geometry : AMS special session, April 29-30, 2006, San Francisco State University, San Francisco, California
（Contemporary mathematics, v. 463）
American Mathematical Society, c2008
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Includes bibliographical references
Description and Table of Contents
Description
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 have led 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 on April 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.
Table of Contents
Results of Cohen-Lenstra type for quadratic function fields by J. D. Achter The hardness of computing an eigenform by E. Bach and D. Charles Constructing elliptic curves of prime order by R. Broker and P. Stevenhagen Space-time codes and non-associative division algebras arising from elliptic curves by A. Deajim and D. Grant Points of low height on $\mathbb{P}^1$ over number fields and bounds for torsion in class groups by J. S. Ellenberg Supersingular genus-2 curves over fields of characteristic 3 by E. W. Howe Search techniques for root-unitary polynomials by K. S. Kedlaya Yet more elements in the Shafarevich-Tate group of the Jacobian of a Fermat curve by B. Levitt and W. McCallum Stable reduction of $X_0(81)$ by K. McMurdy Isomorphism types of commutative algebras of finite rank over an algebraically closed field by B. Poonen A short guide to $p$-torsion of abelian varieties in characteristic $p$ by R. Pries.
by "Nielsen BookData"