Book contents
- Frontmatter
- Contents
- Preface
- Part I Ramification of Henselian Discrete Valuation Fields
- Part II Cyclic Extensions
- 3 Cyclic Extensions of Degree p
- 4 Trace of Differential Forms
- 5 The Hasse–Arf Theorem
- Part III Conductor and Refinements
- Part IV Geometric Applications
- Part V Upper Ramification Subgroups
- Part VI Graded Quotients and Characteristic Forms
- Solutions to Exercises
- References
- Index
5 - The Hasse–Arf Theorem
from Part II - Cyclic Extensions
Published online by Cambridge University Press: 29 May 2026
Book contents
- Frontmatter
- Contents
- Preface
- Part I Ramification of Henselian Discrete Valuation Fields
- Part II Cyclic Extensions
- 3 Cyclic Extensions of Degree p
- 4 Trace of Differential Forms
- 5 The Hasse–Arf Theorem
- Part III Conductor and Refinements
- Part IV Geometric Applications
- Part V Upper Ramification Subgroups
- Part VI Graded Quotients and Characteristic Forms
- Solutions to Exercises
- References
- Index
Summary
As a preliminary to the proof of the Hasse–Arf theorem in the next chapter, the trace mapping of differential forms with log pole is constructed and studied. The construction is based on a logarithmic variant of that in the book Residues and Duality. In the last section, the general construction is applied to inseparable extensions of fields of positive characteristic.
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- Chapter
- Information
- Ramification Groups of Local Fieldswith Geometric Applications, pp. 133 - 158Publisher: Cambridge University PressPrint publication year: 2026
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