Lectures on Arakelov Geometry, by C Soule, et al. Hardcover First edition 1992

Publisher: Cambridge : Cambridge Univ. Press, 1992.

An account for graduate students of this new technique in diophantine geometry; includes account of higher dimensional theory. This text is based on a graduate course given at Harvard University and is aimed at number theorists and algebraic geometers. Complex analysts and differential geometers will also find in it a clear account of recent results and applications of their subjects to new areas.

Contents: Introduction; 1. Intersection theory on regular schemes; 2. Green currents; 3. Arithmetic Chow groups; 4. Characteristic classes; 5. The determinant of Laplace operators; 6. The determinant of the cohomology; 7. The curvature of the determinant line bundle; 8. The arithmetic Riemann-Roch-Grothendieck theorem; References; Index.