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Ramification Groups of Local Fields出版済み 6-8週間でお届けいたします。
Title: Ramification Groups of Local Fields Subtitle: with Geometric Applications Series: New Mathematical Monographs Author: Saito, Takeshi (University of Tokyo) Publisher: Cambridge University Press ISBN: 9781009617536 Cover: HARDCOVER Date: 2026年06月 DESCRIPTION 局所体の分岐群：幾何学的応用を伴う 本書は、ハッセ・アルフの定理などの古典的な成果とともに、不完全剰余体を伴う局所体の上付き分岐群の最新理論を構築します。本書はlog monogenic extensionsを導入し、主要な公式の新たな証明を提示することで、算術幾何学およびガロア表現論の研究者に不可欠なツールを提供します。 Ramification groups of local fields are essential tools for studying boundary behaviour in geometric objects and the degeneration of Galois representations. This book presents a comprehensive development of the recently established theory of upper ramification groups of local fields with imperfect residue fields, starting from the foundations. It also revisits classical theory, including the Hasse-Arf theorem, and offers an optimal generalisation via log monogenic extensions. The conductor of Galois representations, defined through ramification groups, has numerous geometric applications, notably the celebrated Grothendieck-Ogg-Shafarevich formula. A new proof of the Deligne-Kato formula is also provided; this result plays a pivotal role in the theory of characteristic cycles. With a foundational understanding of commutative rings and Galois theory, graduate students and researchers will be well-equipped to engage with this rich area of arithmetic geometry. A self-contained introduction to the recently established theory of upper ramification groups Presents a geometric application of the conductor of Galois representations with a new proof Offers a reference for the theory of log monogenic extension, which serves as a framework for optimal generalisations of the classical theory TABLE OF CONTENTS Part I. Ramification of Henselian Discrete Valuation Fields: 1. Finite extensions 2. Cohomological ?ltration Part II. Cyclic Extensions: 3. Cyclic extensions of degree 4. Trace of differential forms 5. The Hasse-Arf theorem Part III. Conductor and Refinements: 6. Swan conductor 7. Conductor and differential forms Part IV. Geometric Applications: 8. Grothendieck-Ogg-Shafarevich formula 9. Reduced ?ber theorem 10. Nearby cycles on curves Part V. Upper Ramification Subgroups: 11. Stable integral models 12. Upper rami?cation subgroups 13. Logarithmic variant and Artin-Schreier-Witt extensions Part VI. Graded Quotients and Character-Istic Forms: 14. Graded quotients 15. Characteristic forms 16. Logarithmic characteristic forms and the re?ned Swan con-ductor 最近チェックした商品
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