Documenta Mathematica 2003; 918 pp; hardcover Number: 3 ISBN10: 3936609217 ISBN13: 9783936609219 List Price: US$113 Member Price: US$90.40 Order Code: DOCMATH/3
 This volume is dedicated to Professor Kazuya Kato in acknowledgement of his deep and seminal contribution to number theory and algebraic geometry. The book contains papers on a wide range of topics on the cutting edge of research in arithmetic algebraic geometry, number theory, algebraic geometry, and analysis. Topics covered are zeta functions, \(L\)functions, higher class field theory, ramification theory, local explicit formulas, \(p\)adic Hodge theory, \(p\)adic Galois representation theory, arithmetic of elliptic curves, Iwasawa theory, \(K\)theory of algebraic numbers, algebraic cycles, polylogarithms, logarithmic geometry, RiemannHilbert correspondence, rigid cohomology, and anabelian geometry. The volume also contains a short poem on prime numbers written by Kazuya Kato. The material will be of interest to researchers and students in these and neighboring fields. A publication of Documenta Mathematica. The AMS distributes this series, beginning with volume 3, in the United States, Canada, and Mexico. Published by Documenta Mathematica (Bielefeld, Germany). Now available worldwide from the AMS. Readership Graduate students and research mathematicians interested in number theory and algebraic geometry. Table of Contents  A. Abbes and T. Saito  Ramification of local fields with imperfect residue fields II
 K. Bannai  Specialization of the \(p\)adic polylogarithm to \(p\)th power roots of unity
 L. Berger  Bloch and Kato's exponential map: Three explicit formulas
 S. Bloch and H. Esnault  The additive dilogarithm
 D. Burns and C. Greither  Equivariant Weierstrass preparation and values of \(L\)functions at negative integers
 J. Coates, P. Schneider, and R. Sujatha  Links between cyclotomic and \(GL_2\) Iwasawa theory
 R. F. Coleman  Stable maps of curves
 C. Deninger  Twovariable zeta functions and products
 I. Fesenko  Analysis on arithmetic schemes. I
 J.M. Fontaine  Presque \(C_p\)représentations
 T. Fukaya  Coleman power series for \(K_2\) and \(p\)adic zeta functions of modular forms
 Y. Hachimori and O. Venjakob  Completely faithful selmer groups over Kummer extensions
 U. Jannsen and S. Saito  Kato homology of arithmetic schemes and higher class field theory over local fields
 M. Kurihara  On the structure of ideal class groups of CMfields
 N. Kurokawa, H. Ochiai, and M. Wakayama  Absolute derivations and zeta functions
 B. Mazur and K. Rubin  Studying the growth of MordellWeil
 S. Mochizuki  The absolute anabelian geometry of canonical curves
 H. Moon and Y. Taguchi  Refinement of Tate's discriminant bound and nonexistence theorems for mod \(p\) Galois representations
 A. Ogus  On the logarithmic RiemannHilbert correspondence
 B. PerrinRiou  Groupes de Selmer et accouplements; cas particulier des courbes elliptiques
 C. Soulé  A bound for the torsion in the \(K\)theory of algebraic integers
 A. Tamagawa  Unramified Skolem problems and unramified arithmetic Bertini theorems in positive characteristic
 T. Tsuji  On the maximal unramified quotients of \(p\)adic Étale cohomology groups and logarithmic HodgeWitt sheaves
 N. Tsuzuki  On base change theorem and coherence in rigid cohomology
