Book contents
- Frontmatter
- Contents
- Preface
- Part I Ramification of Henselian Discrete Valuation Fields
- 1 Finite Extensions
- 2 Cohomological Filtration
- 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
- Solutions to Exercises
- References
- Index
1 - Finite Extensions
from Part I - Ramification of Henselian Discrete Valuation Fields
Published online by Cambridge University Press: 29 May 2026
Book contents
- Frontmatter
- Contents
- Preface
- Part I Ramification of Henselian Discrete Valuation Fields
- 1 Finite Extensions
- 2 Cohomological Filtration
- 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
- Solutions to Exercises
- References
- Index
Summary
After presenting motivating examples, cyclotomic extensions, the relation between the conductor of Galois representations and the level of the corresponding automorphic forms, and the Grothendieck–Ogg–Shafarevich formula, we sketch the fact that fundamental properties of the main objects of the book, lower and upper ramification groups, show sharp contrasts. The structure of the book together with the content of each chapter are explained. Required backgrounds are also listed.
Keywords
Information
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- Information
- Ramification Groups of Local Fieldswith Geometric Applications, pp. 2 - 55Publisher: Cambridge University PressPrint publication year: 2026
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