Foundations of Rigid Geometry I
Seiten
2018
EMS Press (Verlag)
978-3-03719-135-4 (ISBN)
EMS Press (Verlag)
978-3-03719-135-4 (ISBN)
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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 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.
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.
| Erscheinungsdatum | 31.01.2018 |
|---|---|
| Reihe/Serie | EMS Monographs in Mathematics |
| Sprache | englisch |
| Maße | 165 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | birational geometry • Formal geometry • rigid geometry |
| ISBN-10 | 3-03719-135-X / 303719135X |
| ISBN-13 | 978-3-03719-135-4 / 9783037191354 |
| Zustand | Neuware |
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