Perfectoid Spaces

This book provides an advanced introduction to Peter Scholze's perfectoid spaces and their applications, covering topics such as representations mod p, lifting of modular forms, completed cohomology, local Langlands program, and special values of L-functions.

Format: Paperback / softback
Length: 389 pages
Publication date: 23 April 2023
Publisher: Springer Verlag, Singapore

This book is a comprehensive exploration of perfectoid spaces, a groundbreaking concept developed by Peter Scholze in his groundbreaking work that earned him the prestigious Fields Medal. Presented at the "Perfectoid Spaces" conference held at the International Centre for Theoretical Sciences in Bengaluru, India, from September 9 to 20, 2019, these contributions showcase the latest advancements in Scholze's theory. The primary objective of this book is to provide a sophisticated introduction to Scholze's theory, while also delving into the intricate relationship between perfectoid spaces and various aspects of arithmetic of modular forms. These include representations mod p, lifting of modular forms, completed cohomology, the local Langlands program, and the study of special values of L-functions.

Each chapter in this book is authored by renowned experts in the field of arithmetic geometry, ensuring that readers gain a deep understanding of the subject matter. The content is designed to facilitate future research in this dynamic and rapidly evolving field.

Perfectoid spaces have emerged as a powerful tool in the study of arithmetic geometry, offering a new perspective on classical problems and opening up exciting avenues for research. This book serves as a valuable resource for scholars and researchers seeking to delve deeper into the world of perfectoid spaces and their applications.

Weight: 611g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811671234
Edition number: 1st ed. 2022