Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It of

This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools

Based on lectures presented in courses on algebraic geometry taught by the author at Purdue University, this book covers various topics in the theory of algebra

The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mat

Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimens