
Hardcover ISBN: | 978-3-03719-135-4 |
Product Code: | EMSMONO/7 |
List Price: | $119.00 |
AMS Member Price: | $95.20 |

Hardcover ISBN: | 978-3-03719-135-4 |
Product Code: | EMSMONO/7 |
List Price: | $119.00 |
AMS Member Price: | $95.20 |
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Book DetailsEMS Monographs in MathematicsVolume: 7; 2018; 863 ppMSC: 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.
ReadershipGraduate students and researchers interested in algebraic and arithmetic geometry.
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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. 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.
Graduate students and researchers interested in algebraic and arithmetic geometry.