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
- Appendix A Picard–Fuchs modules
- Appendix B Rigid cohomology
- Appendix C p-adic Hodge theory
- References
- Index of notation
- Subject index
Appendix C - p-adic Hodge 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
- Appendix A Picard–Fuchs modules
- Appendix B Rigid cohomology
- Appendix C p-adic Hodge theory
- References
- Index of notation
- Subject index
Summary
For our last application, we turn to the subject of p-adic Hodge theory. Recall that in Chapter 19, we described a “nonabelian Artin–Schreier” construction, giving an equivalence of categories between continuous representations of the absolute Galois group of a positive characteristic local field on a p-adic vector space and certain differential modules with Frobenius structures. In this appendix, we describe an analogous construction for the Galois group of a mixed-characteristic local field. We also mention a couple of applications of this construction.
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- p-adic Differential Equations , pp. 460 - 468Publisher: Cambridge University PressPrint publication year: 2022