Séminaires et Congrès 2011; 225 pp; softcover Number: 21 ISBN10: 2856292798 ISBN13: 9782856292792 List Price: US$60 Member Price: US$48 Order Code: SECO/21
 The Conference on Arithmetics, Geometry, and Coding Theory was held at the International Center of Mathematical Meetings of Luminy (CIRM) in Marseilles from September 2630, 2005. The conference focused on the interaction between number theory and algebraic geometry and the interaction between coding theory and cryptography. It addressed such subjects as curves covered by the Hermitian curve, towers of function fields, bilinear complexity of the multiplication in the finite fields, codes on various varieties, estimate of the Picard number of surfaces via \(p\)adic cohomology, minimal distance of codes on a surface, and the EulerKronecker constant on global fields. Public key cryptography provided an opportunity for talks on curves and their jacobians: jacobians of \(C_{ab}\) curves, a CRT algorithm to construct genus 2 curves over finite fields, hyperelliptic jacobians and the Steinberg representations. Other talks were devoted to the relations between the enumerator polynomial of codes and modular forms and to a similar construction with construction A of lattices from binary codes to build convolutional codes starting from block codes. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in number theory. Table of Contents  K. Betsumiya and Y. Choie  Invariant ring of CliffordWeil group and Jacobi forms over totally real field
 R. Blache, J. E. Sarlabous, and M. Petkova  A geometric interpretation of reduction in the Jacobians of \(C_{ab}\) curves
 A. Garcia and F. Torres  On unramified coverings of maximal curves
 G. M. Hana  Schubert unions and codes on lstep flag varieties
 M. Giulietti, J. W. P. Hirschfeld, G. Korchmáros, and F. Torres  A family of curves covered by the Hermitian curve
 Y. Ihara  The EulerKronecker invariants in various families of global fields
 J. P. Hansen, T. Johnsen, and K. Ranestad  Grassman codes and Schubert unions
 T. G. Abbott, K. S. Kedlaya, and D. Roe  Bounding Picard numbers of surfaces using \(p\)adic cohomology
 K. Eisenträger and K. Lauter  A CRT algorithm for constructing genus 2 curves over finite fields
 T. Nakashima  Relative ReedMuller codes on projective bundles
 S. Ballet, D. Le Brigand, and R. Rolland  On an application of the definition field descent of a tower of function fields
 P. Solé  Construction A for convolutional codes
 J. F. Volochi and M. Zarzar  Algebraic geometric codes on surfaces
 Y. G. Zarhin  Hyperelliptic jacobians and Steinberg representations
