books by Kazuya Kato (translations mathematics classifying)

books by Kazuya Kato

books:

Arithmetic Algebraic Geometry: Lectures given at the 2nd Session of the Centro Internazionale Matematico ...
Jean-Louis Colliot-Thelene, Kazuya Kato, ...

Springer, 1994

This volume contains three long lecture series by J.L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their topics are respectively the connection between algebraic K-theory and the torsion algebraic cycles on an algebraic variety, a new approach to Iwasawa theory for Hasse-Weil L-function, and the applications of arithemetic geometry to Diophantine approximation. They contain many new results at a very advanced level, but also surveys of the state ...

Kenkichi Iwasawa Collected Papers: Volume 1, 2

Springer, 2001

Kenkichi Iwasawa is one of the most original and influential mathematicians in the 20-th century. He made a number of fundamental contributions in group theory and algebraic number theory. In group theory, he created the theory of (L)-groups (including the structure theorem called "Iwasawa decomposition"), which played an important role in the solution of Hilbert's Fifth Problem. In number theory, he constructed a beautiful theory on ...

Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) (Annals of Mathematics Studies)
Kazuya Kato, Sampei Usui

Princeton University Press, 2009

In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure. The book focuses on two principal topics. First, Kato and Usui construct the fine moduli ...

Number Theory 1: Fermat's Dream (Translations of Mathematical Monographs)

2 reviews
Kazuya Kato, Nobushige Kurokawa, ...

American Mathematical Society, 2000

An accessible path from numbers to the sophisticated methods
This brilliant précis of algebraic number theory goes from the simplest basics up to suggestive outline proofs of the most important theorems. It is probably not a good first book on the subject although it is pretty self-contained in principle. You should already be comfortable with groups, rings, and fields. Its great strength is connecting easily stated questions about Diophantine ...