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
- 11Stable Integral Models
- 12Upper Ramification Subgroups
- 13Logarithmic Variant and Artin–Schreier–Witt Extensions
- Part VIGraded Quotients and Characteristic Forms
- Solutions to Exercises
- References
- Index
13 - Logarithmic Variant and Artin–Schreier–Witt Extensions
from Part V - Upper Ramification Subgroups
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
- 11Stable Integral Models
- 12Upper Ramification Subgroups
- 13Logarithmic Variant and Artin–Schreier–Witt Extensions
- Part VIGraded Quotients and Characteristic Forms
- Solutions to Exercises
- References
- Index
Summary
Replacing immersions to smooth schemes by exact immersions to log smooth schemes, we define a logarithmic variant of the filtration by upper ramification subgroups. As a preliminary, we prepare basic facts on log smooth schemes. The logarithmic variant coincides with the non-logarithmic one after taking a log smooth base extension. For abelian extensions in characteristic p, the filtration is given by Brylinski's filtration on the Witt vectors. The proof is based on a computation of Witt vectors with respect to dilatations.
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- Information
- Ramification Groups of Local Fieldswith Geometric Applications, pp. 307 - 334Publisher: Cambridge University PressPrint publication year: 2026
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