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A Collection of Manuscripts Written in Honour of Kazuya Kato on the Occasion of His Fiftieth Birthday
Edited by: S. Bloch, University of Chicago, IL, I. Fesenko, University of Nottingham, England, L. Illusie, University of Paris-Sud, Orsay, France, M. Kurihara, Tokyo Metropolitan University, Japan, S. Saito, Nagoya University, Japan, T. Saito, University of Tokyo, Japan, and P. Schneider, Westfalische Wilhems University, Muenster, Germany
A publication of Documenta Mathematica (Bielefeld, Germany).
Documenta Mathematica
2003; 918 pp; hardcover
Number: 3
ISBN-10: 3-936609-21-7
ISBN-13: 978-3-936609-21-9
List Price: US$113
Member Price: US$90.40
Order Code: DOCMATH/3
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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, Riemann-Hilbert 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.


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 -- Two-variable 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 CM-fields
  • N. Kurokawa, H. Ochiai, and M. Wakayama -- Absolute derivations and zeta functions
  • B. Mazur and K. Rubin -- Studying the growth of Mordell-Weil
  • S. Mochizuki -- The absolute anabelian geometry of canonical curves
  • H. Moon and Y. Taguchi -- Refinement of Tate's discriminant bound and non-existence theorems for mod \(p\) Galois representations
  • A. Ogus -- On the logarithmic Riemann-Hilbert correspondence
  • B. Perrin-Riou -- 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 Hodge-Witt sheaves
  • N. Tsuzuki -- On base change theorem and coherence in rigid cohomology
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