Softcover ISBN:  9780821843208 
Product Code:  CONM/463 
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MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821881422 
Product Code:  CONM/463.E 
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MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821843208 
eBook: ISBN:  9780821881422 
Product Code:  CONM/463.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 
Softcover ISBN:  9780821843208 
Product Code:  CONM/463 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821881422 
Product Code:  CONM/463.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821843208 
eBook ISBN:  9780821881422 
Product Code:  CONM/463.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 

Book DetailsContemporary MathematicsVolume: 463; 2008; 129 ppMSC: Primary 14; 11
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.
ReadershipGraduate students and research mathematicians interested in arithmetic geometry and computational number theory.

Table of Contents

Articles

Jeffrey D. Achter — Results of CohenLenstra type for quadratic function fields [ MR 2459984 ]

Eric Bach and Denis Charles — The hardness of computing an eigenform [ MR 2459985 ]

Reinier Bröker and Peter Stevenhagen — Constructing elliptic curves of prime order [ MR 2459986 ]

Abdulaziz Deajim and David Grant — Spacetime codes and nonassociative division algebras arising from elliptic curves [ MR 2459987 ]

Jordan S. Ellenberg — Points of low height on $\Bbb P^1$ over number fields and bounds for torsion in class groups [ MR 2459988 ]

Everett W. Howe — Supersingular genus2 curves over fields of characteristic 3 [ MR 2459989 ]

Kiran S. Kedlaya — Search techniques for rootunitary polynomials [ MR 2459990 ]

Benjamin Levitt and William McCallum — Yet more elements in the ShafarevichTate group of the Jacobian of a Fermat curve [ MR 2459991 ]

Ken McMurdy — Stable reduction of $X_0(81)$ [ MR 2459992 ]

Bjorn Poonen — Isomorphism types of commutative algebras of finite rank over an algebraically closed field [ MR 2459993 ]

Rachel Pries — A short guide to $p$torsion of abelian varieties in characteristic $p$ [ MR 2459994 ]


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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.
Graduate students and research mathematicians interested in arithmetic geometry and computational number theory.

Articles

Jeffrey D. Achter — Results of CohenLenstra type for quadratic function fields [ MR 2459984 ]

Eric Bach and Denis Charles — The hardness of computing an eigenform [ MR 2459985 ]

Reinier Bröker and Peter Stevenhagen — Constructing elliptic curves of prime order [ MR 2459986 ]

Abdulaziz Deajim and David Grant — Spacetime codes and nonassociative division algebras arising from elliptic curves [ MR 2459987 ]

Jordan S. Ellenberg — Points of low height on $\Bbb P^1$ over number fields and bounds for torsion in class groups [ MR 2459988 ]

Everett W. Howe — Supersingular genus2 curves over fields of characteristic 3 [ MR 2459989 ]

Kiran S. Kedlaya — Search techniques for rootunitary polynomials [ MR 2459990 ]

Benjamin Levitt and William McCallum — Yet more elements in the ShafarevichTate group of the Jacobian of a Fermat curve [ MR 2459991 ]

Ken McMurdy — Stable reduction of $X_0(81)$ [ MR 2459992 ]

Bjorn Poonen — Isomorphism types of commutative algebras of finite rank over an algebraically closed field [ MR 2459993 ]

Rachel Pries — A short guide to $p$torsion of abelian varieties in characteristic $p$ [ MR 2459994 ]