Bruhat–Tits Theory

This comprehensive book introduces Bruhat–Tits theory, offering insights for both researchers and graduate students in related fields.

This book serves as the first comprehensive resource in English dedicated to Bruhat–Tits theory, a significant area within number theory, representation theory, and algebraic geometry. It provides a detailed exploration of the subject, making it a valuable reference for seasoned researchers and an accessible introduction for graduate students and early career mathematicians alike.

The text is organized into several parts, beginning with a review of essential background material, including Lie theory, metric geometry, algebraic groups, and integral models. This foundational knowledge sets the stage for a thorough examination of the core aspects of Bruhat–Tits theory, presented in a clear and motivated manner. The axiomatic summary included is particularly useful for understanding the main applications of the theory.

In addition to the fundamental concepts, the book delves into modern topics that are currently relevant in research, ensuring that readers are equipped with the latest developments in the field. Practical applications of the theory are also illustrated, providing concrete examples that enhance comprehension. The appendices offer further insights into integral models, making this book a well-rounded resource for anyone interested in the nuances of Bruhat–Tits theory.