Ramification Groups of Local Fields: with Geometric Applications (New Mathematical Monographs, Series Number 53) - Hardcover
Synopsis
Fully develops the theory of ramification groups from the foundations, spanning classical theory to recent developments.
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About the Author
Takeshi Saito is a Professor of Mathematics at School of Mathematical Sciences, the University of Tokyo, specialising in arithmetic geometry. He is the recipient of the Algebra Prize of the Mathematical Society of Japan (1998) and Spring Prize of the Mathematical Society of Japan (2001) and is the Israel Gelfand Chair in Mathematics at IHES (2024–2026).
"About this title" may belong to another edition of this title.
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Ramification Groups of Local Fields: with Geometric Applications (New Mathematical Monographs, Series Number 53)
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Ramification Groups Of Local Fields: With Geometric Applications
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Ramification Groups of Local Fields (Hardcover)
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Hardcover. Condition: new. Hardcover. 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 HasseArf 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 GrothendieckOggShafarevich formula. A new proof of the DeligneKato 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. This book develops the modern theory of upper ramification groups for local fields with imperfect residue fields, alongside classical results like the HasseArf theorem. It introduces log monogenic extensions and provides new proofs of key formulas, offering essential tools for researchers in arithmetic geometry and Galois representation theory. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Seller Inventory # 9781009617536
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Ramification Groups of Local Fields: with Geometric Applications (New Mathematical Monographs, Series Number 53)
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Ramification Groups Of Local Fields: With Geometric Applications
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Ramification Groups of Local Fields: with Geometric Applications (New Mathematical Monographs, Series Number 53)
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Ramification Groups of Local Fields: with Geometric Applications (New Mathematical Monographs)
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Ramification Groups of Local Fields
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9781009617536
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Ramification Groups of Local Fields
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Buch. Condition: Neu. Ramification Groups of Local Fields | Takeshi Saito | Buch | Englisch | 2026 | Cambridge University Press | EAN 9781009617536 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand. Seller Inventory # 135574343
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Ramification Groups of Local Fields: with Geometric Applications (New Mathematical Monographs)
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