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
24 - The Berkovich projective line
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 chapter, we make the definition of the Gelfand spectrum explicit in the case of the ring of power series convergent on a closed disc or annulus. This will lead us to the construction of the projective line over ?? in the Berkovich approach to nonarchimedean algebraic geometry.
- Type
- Chapter
- Information
- p-adic Differential Equations , pp. 399 - 410Publisher: Cambridge University PressPrint publication year: 2022