Algorithmic Arithmetic, Geometry, and Coding Theory

This volume contains the proceedings of the 14th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held June 3-7, 2013, at CIRM, Marseille, France. These international conferences, held every two years, have been a major event in the area of algorithmic and applied arithmetic geometry for more than 20 years. This volume contains 13 original research articles covering geometric error correcting codes, and algorithmic and explicit arithmetic geometry of curves and higher dimensional varieties. Tools used in these articles include classical algebraic geometry of curves, varieties and Jacobians, Suslin homology, Monsky-Washnitzer cohomology, and $L$-functions of modular forms.

Table of Contents

Chapter 1 Geometric Error Correcting Codes
Chapter 2 Algorithmic: Special Varieties
Chapter 3 Algorithmic: Point Counting
Chapter 4 Algorithmic: General
Chapter 5 Explicit Algebraic Geometry
Chapter 6 Arithmetic Geometry