Arithmetic Algebraic Geometry [electronic resource] : Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Trento, Italy, June 24–July 2, 1991 / by Jean-Louis Colliot-Thélène, Kazuya Kato, Paul Vojta ; edited by Edoardo Ballico.

Cycles algébriques de torsion et K-théorie algébrique Cours au C.I.M.E., juin 1991 -- Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions via BdR. Part I -- Applications of arithmetic algebraic geometry to diophantine approximations -- Arithmetic algebraic geometry, Trento, Italy 1991.

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.