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Softcover ISBN:  9780821890202 
Product Code:  SURV/33.S 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470412609 
Product Code:  SURV/33.S.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821890202 
eBook ISBN:  9781470412609 
Product Code:  SURV/33.S.B 
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MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 33; 1990; 169 ppMSC: Primary 12; 32; 14; 20; 46; Secondary 47
The purpose of this book is to introduce a new notion of analytic space over a nonArchimedean field. Despite the total disconnectedness of the ground field, these analytic spaces have the usual topological properties of a complex analytic space, such as local compactness and local arcwise connectedness. This makes it possible to apply the usual notions of homotopy and singular homology. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of BruhatTits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space. Geometrical considerations are used to obtain some applications, and the analytic spaces are used to construct the foundations of a nonArchimedean spectral theory of bounded linear operators. This book requires a background at the level of basic graduate courses in algebra and topology, as well as some familiarity with algebraic geometry. It would be of interest to research mathematicians and graduate students working in algebraic geometry, number theory, and \(p\)adic analysis.

Table of Contents

Chapters

Introduction

1. The spectrum of a commutative Banach ring

2. Affinoid spaces

3. Analytic spaces

4. Analytic curves

5. Analytic groups and buildings

6. The homotopy type of certain analytic spaces

7. Spectral theory

8. Perturbation theory

9. The dimension of a Banach algebra


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The purpose of this book is to introduce a new notion of analytic space over a nonArchimedean field. Despite the total disconnectedness of the ground field, these analytic spaces have the usual topological properties of a complex analytic space, such as local compactness and local arcwise connectedness. This makes it possible to apply the usual notions of homotopy and singular homology. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of BruhatTits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space. Geometrical considerations are used to obtain some applications, and the analytic spaces are used to construct the foundations of a nonArchimedean spectral theory of bounded linear operators. This book requires a background at the level of basic graduate courses in algebra and topology, as well as some familiarity with algebraic geometry. It would be of interest to research mathematicians and graduate students working in algebraic geometry, number theory, and \(p\)adic analysis.

Chapters

Introduction

1. The spectrum of a commutative Banach ring

2. Affinoid spaces

3. Analytic spaces

4. Analytic curves

5. Analytic groups and buildings

6. The homotopy type of certain analytic spaces

7. Spectral theory

8. Perturbation theory

9. The dimension of a Banach algebra