Title: 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