Book contents
- Frontmatter
- Contents
- Preface
- Part IRamification of Henselian Discrete Valuation Fields
- Part IICyclic Extensions
- Part IIIConductor and Refinements
- Part IVGeometric Applications
- 8Grothendieck–Ogg–Shafarevich Formula
- 9Reduced Fiber Theorem
- 10Nearby Cycles on Curves
- Part VUpper Ramification Subgroups
- Part VIGraded Quotients and Characteristic Forms
- Solutions to Exercises
- References
- Index
9 - Reduced Fiber Theorem
from Part IV - Geometric Applications
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
- 8Grothendieck–Ogg–Shafarevich Formula
- 9Reduced Fiber Theorem
- 10Nearby Cycles on Curves
- Part VUpper Ramification Subgroups
- Part VIGraded Quotients and Characteristic Forms
- Solutions to Exercises
- References
- Index
Summary
The reduced fiber theorem asserts that a scheme of finite type over a discrete valuation ring has a reduced closed fiber after taking a suitable base change and normalization. This is deduced from the study of cyclic extensions of degree p in Chapter 3. It is also an essential ingredient in the construction of upper ramification groups in Chapter 12.
Information
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- Chapter
- Information
- Ramification Groups of Local Fieldswith Geometric Applications, pp. 215 - 229Publisher: Cambridge University PressPrint publication year: 2026
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