Arithmetic algebraic geometry

Description:

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 of the art on the subject with complete, detailed profs and a lot of background. Hence they can be useful to readers with very different background and experience. CONTENTS: J.L. Colliot-Thelene: Cycles algebriques de torsion et K-theorie algebrique.- K. Kato: Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions.- P. Vojta: Applications of arithmetic algebraic geometry to diophantine approximations.

subjects: Arithmetical algebraic geometry,  Algebraic geometry,  Analytic geometry,  Geometry - Algebraic,  Number Theory,  Algebraic Cycles,  Arakelov Theory,  Arithmetic Geometry,  Diophantine Approximation,  L-functions,  Mathematics / Geometry / Algebraic,  Mathematics,  Geometrie algebrique arithmetique,  Algebrai˜sche meetkunde,  Geometria Algebrica,  Geometry, algebraic