Perfectoid Spaces

 
Edition number: 1st ed. 2022
Publisher: Springer
Date of Publication:
Number of Volumes: 1 pieces, Book
 
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Product details:

ISBN13:9789811671234
ISBN10:98116712311
Binding:Paperback
No. of pages:389 pages
Size:235x155 mm
Weight:611 g
Language:English
Illustrations: IX, 389 p.
606
Category:
Short description:

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.

Long description:
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.
Table of Contents:
On ?-Lattices in Modular (?, ?)-Modules.- The Relative (De-)Perfectoidification Functor and Motivic P-Adic Cohomologies.- Diagrams and Mod p Representations of p-Adic Groups.- A Short Review on Local Shtukas and Divisible Local Anderson Modules.- An Introduction to p-Adic Hodge Theory.- Perfectoid Spaces: An Annotated Bibliography.- The Fargues?Fontaine Curve and p-Adichodgetheory.- Simplicial Galois Deformation Functors.