Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 0 Introductory remarks
- Part I Tools of p-adic Analysis
- Part II Differential Algebra
- Part III p-adic Differential Equations on Discs and Annuli
- Part IV Difference Algebra and Frobenius Modules
- Part V Frobenius Structures
- Part VI The p-adic local monodromy theorem
- Part VII Global theory
- 23 Banach rings and their spectra
- 24 The Berkovich projective line
- 25 Convergence polygons
- 26 Index theorems
- 27 Local constancy at type-4 points
- Appendix A Picard–Fuchs modules
- Appendix B Rigid cohomology
- Appendix C p-adic Hodge theory
- References
- Index of notation
- Subject index
23 - Banach rings and their spectra
from Part VII - Global theory
Published online by Cambridge University Press: 06 August 2022
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 0 Introductory remarks
- Part I Tools of p-adic Analysis
- Part II Differential Algebra
- Part III p-adic Differential Equations on Discs and Annuli
- Part IV Difference Algebra and Frobenius Modules
- Part V Frobenius Structures
- Part VI The p-adic local monodromy theorem
- Part VII Global theory
- 23 Banach rings and their spectra
- 24 The Berkovich projective line
- 25 Convergence polygons
- 26 Index theorems
- 27 Local constancy at type-4 points
- Appendix A Picard–Fuchs modules
- Appendix B Rigid cohomology
- Appendix C p-adic Hodge theory
- References
- Index of notation
- Subject index
Summary
In this final part of the book, we return to the study of convergence of solutions of differential equations from Part III, but this time taking a more global viewpoint. In this chapter, we introduce the key concept of the Gelfand spectrum associated to a (commutative) Banach ring. A running theme will be the analogy with the prime (Zariski) spectrum associated to a commutative ring.
- Type
- Chapter
- Information
- p-adic Differential Equations , pp. 393 - 398Publisher: Cambridge University PressPrint publication year: 2022