这本书包含关于完美空间、它们的介绍和应用的精选章节，正如彼得·斯科尔茨在他的菲尔兹获奖作品中所发明的那样。这些贡献将在2019年9月9日至20日在印度班加罗尔国际理论科学中心举行的“完美空间”会议上发表。本书的目的是对Scholze的理论进行深入介绍，并理解完形空间与模（或更一般地说，自守）形式算术的某些方面之间的关系，如模p的表示、模形式的提升、完全上同调、局部Langland程序和L-函数的特殊值。所有章节都由算术几何领域的专家撰写，这将有助于该方向的未来研究。
Perfectoid Spaces
This book contains selected chapters on perfectoid spaces, their introduction and applications, as invented by Peter Scholze in his Fields Medal winning work. These contributions are presented at the conference on “Perfectoid Spaces” held at the International Centre for Theoretical Sciences, Bengaluru, India, from 9–20 September 2019. The objective of the book is to give an advanced introduction to Scholze’s theory and understand the relation between perfectoid spaces and some aspects of arithmetic of modular (or, more generally, automorphic) forms such as representations mod p, lifting of modular forms, completed cohomology, local Langlands program, and special values of L-functions. All chapters are contributed by experts in the area of arithmetic geometry that will facilitate future research in the direction.
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