Book contents
- Frontmatter
- Contents
- Preface
- Part I Ramification of Henselian Discrete Valuation Fields
- Part II Cyclic Extensions
- Part III Conductor and Refinements
- Part IV Geometric Applications
- Part V Upper Ramification Subgroups
- Part VI Graded Quotients and Characteristic Forms
- 14 Graded Quotients
- 15 Characteristic Forms
- 16 Logarithmic Characteristic Forms and the Refined Swan Conductor
- Solutions to Exercises
- References
- Index
15 - Characteristic Forms
from Part VI - Graded Quotients and Characteristic Forms
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
- Part III Conductor and Refinements
- Part IV Geometric Applications
- Part V Upper Ramification Subgroups
- Part VI Graded Quotients and Characteristic Forms
- 14 Graded Quotients
- 15 Characteristic Forms
- 16 Logarithmic Characteristic Forms and the Refined Swan Conductor
- Solutions to Exercises
- References
- Index
Summary
We construct an injection from the dual of the graded quotients of upper ramification groups to a twisted homology group of the cotangent complex. We call the injection the characteristic form. The construction is given in the case where the characteristic is p and the index is an integer. In the geometric case, the construction is based on the group structure on the boundary of the dilatation obtained from the groupoid structure of the self products.
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- Ramification Groups of Local Fieldswith Geometric Applications, pp. 366 - 394Publisher: Cambridge University PressPrint publication year: 2026
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