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
14 - Graded Quotients
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
From this chapter on, we study graded quotients of upper ramification subgroups. In this chapter we prove that the graded quotients are abelian and annihilated by p. The proof is by reduction to the classical case where the extension is totally ramified. The geometric fact behind this property is that the closed fiber of the covering of stable integral models is étale. Other tools used in the proof of the reduction are the first homology group of the cotangent complex and the Tor group of the module of relative differential forms.
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- Ramification Groups of Local Fieldswith Geometric Applications, pp. 336 - 365Publisher: Cambridge University PressPrint publication year: 2026
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