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

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

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

​​​​This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry.

The authors give the complete stably rational classification of algebraic tori of dimensions and over a field . In particular, the stably rational classificatio