Bruhat-Tits Theory: A New Approach

Bruhat-Tits theory is an important topic in number theory, representation theory, harmonic analysis, and algebraic geometry. This book gives the first comprehensive treatment of this theory over 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 gives a review of the relevant background material, touching upon Lie theory, metric geometry, algebraic groups, and integral models. Part II gives a complete, detailed, and motivated treatment of the core theory as well as an axiomatic summary of Bruhat-Tits theory that suffices for the main applications. Part III treats modern topics that have become important in current research. Part IV provides a few sample applications of the theory. The appendices contain further details on the topic of integral models, including a detailed study of integral models.

Bruhat-Tits理論是數論、表示論、調和分析和代數幾何中的重要主題。本書首次全面介紹了在離散值Henselian場上的這一理論。它既可作為該領域研究人員的參考資料，也可作為研究生和初級職業數學家的全面入門。書的第一部分回顧了相關背景材料，涉及李理論、度量幾何、代數群和整數模型。第二部分對核心理論進行了完整、詳細和有動機的處理，並提供了足夠應用的Bruhat-Tits理論的公理摘要。第三部分介紹了當前研究中變得重要的現代主題。第四部分提供了該理論的一些樣本應用。附錄中包含了有關整數模型的進一步細節，包括對整數模型的詳細研究。