This quantity includes 3 lengthy lecture sequence via J.L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their issues are respectively the relationship among algebraic K-theory and the torsion algebraic cycles on an algebraic kind, a brand new method of Iwasawa conception for Hasse-Weil L-function, and the functions of arithemetic geometry to Diophantine approximation. They comprise many new effects at a truly complex point, but in addition surveys of the state-of-the-art at the topic with entire, certain profs and many historical past. therefore they are often necessary to readers with very various historical past and event. CONTENTS: J.L. Colliot-Thelene: Cycles algebriques de torsion et K-theorie algebrique.- okay. Kato: Lectures at the method of Iwasawa conception for Hasse-Weil L-functions.- P. Vojta: purposes of mathematics algebraic geometry to diophantine approximations.

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