Book contents
- Frontmatter
- Contents
- Preface
- Part IRamification of Henselian Discrete Valuation Fields
- Part IICyclic Extensions
- Part IIIConductor and Refinements
- Part IVGeometric Applications
- Part VUpper Ramification Subgroups
- Part VIGraded Quotients and Characteristic Forms
- 14Graded Quotients
- 15Characteristic Forms
- 16Logarithmic Characteristic Forms and the Refined Swan Conductor
- Solutions to Exercises
- References
- Index
16 - Logarithmic Characteristic Forms and the Refined Swan Conductor
from Part VI - Graded Quotients and Characteristic Forms
Published online by Cambridge University Press: 29 May 2026
Book contents
- Frontmatter
- Contents
- Preface
- Part IRamification of Henselian Discrete Valuation Fields
- Part IICyclic Extensions
- Part IIIConductor and Refinements
- Part IVGeometric Applications
- Part VUpper Ramification Subgroups
- Part VIGraded Quotients and Characteristic Forms
- 14Graded Quotients
- 15Characteristic Forms
- 16Logarithmic Characteristic Forms and the Refined Swan Conductor
- Solutions to Exercises
- References
- Index
Summary
We introduce a logarithmic variant of the characteristic form. In the case of abelian extensions, we prove the equality of the filtration by the logarithmic upper ramification groups and cohomological filtration.The logarithmic characteristic form is the same as the refined Swan conductor up to the sign. In the positive characteristic case, the existence of the refined Swan conductor is reduced to computations of Witt vectors. At the end of the book, we give a brief summary of Kato's proof of the existence of the refined Swan conductor in the mixed characteristic case.
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- Ramification Groups of Local Fieldswith Geometric Applications, pp. 395 - 420Publisher: Cambridge University PressPrint publication year: 2026
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