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Perfectoid Spaces: Lectures from the 2017 Arizona Winter School
 
Bhargav Bhatt University of Michigan, Ann Arbor, MI
Edited by: Bryden Cais University of Arizona, Tucson, AZ
Ana Caraiani Imperial College, London, United Kingdom
Kiran S. Kedlaya University of California, San Diego, La Jolla, CA
Peter Scholze University of Bonn, Bonn, Germany
Jared Weinstein Boston University, Boston, MA
Perfectoid Spaces
Softcover ISBN:  978-1-4704-6510-0
Product Code:  SURV/242.S
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-5411-1
Product Code:  SURV/242.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6510-0
eBook: ISBN:  978-1-4704-5411-1
Product Code:  SURV/242.S.B
List Price: $184.00 $141.50
MAA Member Price: $165.60 $127.35
AMS Member Price: $147.20 $113.20
Perfectoid Spaces
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Perfectoid Spaces: Lectures from the 2017 Arizona Winter School
Bhargav Bhatt University of Michigan, Ann Arbor, MI
Edited by: Bryden Cais University of Arizona, Tucson, AZ
Ana Caraiani Imperial College, London, United Kingdom
Kiran S. Kedlaya University of California, San Diego, La Jolla, CA
Peter Scholze University of Bonn, Bonn, Germany
Jared Weinstein Boston University, Boston, MA
Softcover ISBN:  978-1-4704-6510-0
Product Code:  SURV/242.S
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-5411-1
Product Code:  SURV/242.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6510-0
eBook ISBN:  978-1-4704-5411-1
Product Code:  SURV/242.S.B
List Price: $184.00 $141.50
MAA Member Price: $165.60 $127.35
AMS Member Price: $147.20 $113.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2422019; 297 pp
    MSC: Primary 11; 14

    Introduced by Peter Scholze in 2011, perfectoid spaces are a bridge between geometry in characteristic 0 and characteristic \(p\), and have been used to solve many important problems, including cases of the weight-monodromy conjecture and the association of Galois representations to torsion classes in cohomology. In recognition of the transformative impact perfectoid spaces have had on the field of arithmetic geometry, Scholze was awarded a Fields Medal in 2018.

    This book, originating from a series of lectures given at the 2017 Arizona Winter School on perfectoid spaces, provides a broad introduction to the subject. After an introduction with insight into the history and future of the subject by Peter Scholze, Jared Weinstein gives a user-friendly and utilitarian account of the theory of adic spaces. Kiran Kedlaya further develops the foundational material, studies vector bundles on Fargues–Fontaine curves, and introduces diamonds and shtukas over them with a view toward the local Langlands correspondence. Bhargav Bhatt explains the application of perfectoid spaces to comparison isomorphisms in \(p\)-adic Hodge theory. Finally, Ana Caraiani explains the application of perfectoid spaces to the construction of Galois representations associated to torsion classes in the cohomology of locally symmetric spaces for the general linear group.

    This book will be an invaluable asset for any graduate student or researcher interested in the theory of perfectoid spaces and their applications.

    Readership

    Graduate students and researchers interested in new developments in algebraic geometry and algebraic number theory.

  • Table of Contents
     
     
    • Chapters
    • Adic spaces
    • Sheaves, stacks, and shtukas
    • The Hodge-Tate decomposition via perfectoid spaces
    • Perfectoid Shimura varieties
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2422019; 297 pp
MSC: Primary 11; 14

Introduced by Peter Scholze in 2011, perfectoid spaces are a bridge between geometry in characteristic 0 and characteristic \(p\), and have been used to solve many important problems, including cases of the weight-monodromy conjecture and the association of Galois representations to torsion classes in cohomology. In recognition of the transformative impact perfectoid spaces have had on the field of arithmetic geometry, Scholze was awarded a Fields Medal in 2018.

This book, originating from a series of lectures given at the 2017 Arizona Winter School on perfectoid spaces, provides a broad introduction to the subject. After an introduction with insight into the history and future of the subject by Peter Scholze, Jared Weinstein gives a user-friendly and utilitarian account of the theory of adic spaces. Kiran Kedlaya further develops the foundational material, studies vector bundles on Fargues–Fontaine curves, and introduces diamonds and shtukas over them with a view toward the local Langlands correspondence. Bhargav Bhatt explains the application of perfectoid spaces to comparison isomorphisms in \(p\)-adic Hodge theory. Finally, Ana Caraiani explains the application of perfectoid spaces to the construction of Galois representations associated to torsion classes in the cohomology of locally symmetric spaces for the general linear group.

This book will be an invaluable asset for any graduate student or researcher interested in the theory of perfectoid spaces and their applications.

Readership

Graduate students and researchers interested in new developments in algebraic geometry and algebraic number theory.

  • Chapters
  • Adic spaces
  • Sheaves, stacks, and shtukas
  • The Hodge-Tate decomposition via perfectoid spaces
  • Perfectoid Shimura varieties
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.