Foundations of Rigid Geometry I

Released on by Kazuhiro Fujiwara
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  • Foundations of Rigid Geometry I Book Detail

  • Author : Kazuhiro Fujiwara
  • Release Date : 2018
  • Publisher :
  • Genre : MATHEMATICS
  • Pages : 863
  • ISBN 13 : 9783037196359
  • File Size : 94,94 MB
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Foundations of Rigid Geometry I by Kazuhiro Fujiwara PDF Summary

Book Description: 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. Nowadays, 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, putting 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 on 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.

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Foundations of Rigid Geometry I

Foundations of Rigid Geometry I

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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 aime

Lectures on Formal and Rigid Geometry

Lectures on Formal and Rigid Geometry

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The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, t