Bruhat-Tits Theory: A New Approach

The theory of Bruhat-Tits buildings is an important topic in number theory, representation theory, and algebraic geometry. This book, the first in English on the subject, gives a comprehensive account of Bruhat-Tits theory for discretely valued Henselian fields. It can serve both as a reference for researchers in the field and as a thorough introduction for graduate students and early career mathematicians. Part I of the book begins with a review of relevant background material before proceeding to give a complete, detailed, and motivated treatment of the core theory. For more experienced readers looking to learn the essentials for use in their own work, there is also an axiomatic summary of Bruhat-Tits theory that suffices for the main applications. Part II treats modern topics that have become important at the cutting edge of research, while the appendices contain further details on more specialized background material.