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
- 11 Stable Integral Models
- 12 Upper Ramification Subgroups
- 13 Logarithmic Variant and Artin–Schreier–Witt Extensions
- Part VI Graded Quotients and Characteristic Forms
- Solutions to Exercises
- References
- Index
12 - Upper Ramification Subgroups
from Part V - Upper Ramification Subgroups
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
- 11 Stable Integral Models
- 12 Upper Ramification Subgroups
- 13 Logarithmic Variant and Artin–Schreier–Witt Extensions
- Part VI Graded Quotients and Characteristic Forms
- Solutions to Exercises
- References
- Index
Summary
We define filtration by upper ramification subgroups. Using the geometric construction in the previous chapter, we construct a filtration on the fiber functor. The proof of the fact that this filtration defines the subgroups is based on the going down theorem. We prove that the first steps of the filtration are in fact the inertia group and the wild inertia group, using the computation in the monogenic case. We also prove semi-continuity. The proof relies on the stable reduction theorem and a general version of the reduced fiber theorem.
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- Ramification Groups of Local Fieldswith Geometric Applications, pp. 284 - 306Publisher: Cambridge University PressPrint publication year: 2026
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