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Foundations of Rigid Geometry I
 
Kazuhiro Fujiwara Nagoya University, Japan
Fumiharu Kato Tokyo Institute of Technology, Japan
A publication of European Mathematical Society
Foundations of Rigid Geometry I
Hardcover ISBN:  978-3-03719-135-4
Product Code:  EMSMONO/7
List Price: $119.00
AMS Member Price: $95.20
Please note AMS points can not be used for this product
Foundations of Rigid Geometry I
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Foundations of Rigid Geometry I
Kazuhiro Fujiwara Nagoya University, Japan
Fumiharu Kato Tokyo Institute of Technology, Japan
A publication of European Mathematical Society
Hardcover ISBN:  978-3-03719-135-4
Product Code:  EMSMONO/7
List Price: $119.00
AMS Member Price: $95.20
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Monographs in Mathematics
    Volume: 72018; 863 pp
    MSC: Primary 11; Secondary 06; 13; 14

    Rigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate's rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean valued fields. Today rigid geometry is a discipline in its own right and has acquired vast and rich structures based on discoveries of its relationship with birational and formal geometries.

    In this research monograph, foundational aspects of rigid geometry are discussed, with an emphasis on birational and topological features of rigid spaces. Besides the rigid geometry itself, topics include the general theory of formal schemes and formal algebraic spaces, based on a theory of complete rings which are not necessarily Noetherian. Also included is a discussion of the relationship with Tate's original rigid analytic geometry, V. G. Berkovich's analytic geometry, and R. Huber's adic spaces. As a model example of applications, a proof of Nagata's compactification theorem for schemes is given in the appendix. The book is encyclopedic and almost self contained.

    A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

    Readership

    Graduate students and researchers interested in algebraic and arithmetic geometry.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 72018; 863 pp
MSC: Primary 11; Secondary 06; 13; 14

Rigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate's rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean valued fields. Today rigid geometry is a discipline in its own right and has acquired vast and rich structures based on discoveries of its relationship with birational and formal geometries.

In this research monograph, foundational aspects of rigid geometry are discussed, with an emphasis on birational and topological features of rigid spaces. Besides the rigid geometry itself, topics include the general theory of formal schemes and formal algebraic spaces, based on a theory of complete rings which are not necessarily Noetherian. Also included is a discussion of the relationship with Tate's original rigid analytic geometry, V. G. Berkovich's analytic geometry, and R. Huber's adic spaces. As a model example of applications, a proof of Nagata's compactification theorem for schemes is given in the appendix. The book is encyclopedic and almost self contained.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and researchers interested in algebraic and arithmetic geometry.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.