Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine prob

To view the abstract go to http://www.ams.org/books/memo/1166.

The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book i

Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, th