Ramification Groups of Local Fields: with Geometric Applications: 53 (New Mathematical Monographs, Series Number 53) - Tapa dura

Saito, Takeshi

9781009617536: Ramification Groups of Local Fields: with Geometric Applications: 53 (New Mathematical Monographs, Series Number 53)

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ISBN 10: 1009617532 ISBN 13: 9781009617536

Editorial: Cambridge University Press, 2026

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Fully develops the theory of ramification groups from the foundations, spanning classical theory to recent developments.

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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).

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Editorial: Cambridge University Press
A�o de publicaci�n: 2026
Idioma: Ingl�s
ISBN 10: 1009617532
ISBN 13: 9781009617536
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Ramification Groups of Local Fields: with Geometric Applications (New Mathematical Monographs, Series Number 53)

Saito, Takeshi

Publicado por Cambridge University Press, 2026

ISBN 10: 1009617532 ISBN 13: 9781009617536

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Ramification Groups Of Local Fields: With Geometric Applications

Saito, Takeshi (University Of Tokyo)

Publicado por Cambridge University Press, 2026

ISBN 10: 1009617532 ISBN 13: 9781009617536

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Ramification Groups of Local Fields (Hardcover)

Takeshi Saito

Publicado por Cambridge University Press, Cambridge, 2026

ISBN 10: 1009617532 ISBN 13: 9781009617536

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Hardcover. Condici�n: 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. N� de ref. del art�culo: 9781009617536

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Ramification Groups of Local Fields: with Geometric Applications (New Mathematical Monographs, Series Number 53)

Takeshi Saito

Publicado por Cambridge University Press, 2026

ISBN 10: 1009617532 ISBN 13: 9781009617536

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Ramification Groups of Local Fields: with Geometric Applications (New Mathematical Monographs, Series Number 53)

Takeshi Saito

Publicado por Cambridge University Press, 2026

ISBN 10: 1009617532 ISBN 13: 9781009617536

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Ramification Groups of Local Fields: with Geometric Applications (New Mathematical Monographs)

Saito, Takeshi

Publicado por Cambridge University Press, 2026

ISBN 10: 1009617532 ISBN 13: 9781009617536

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Ramification Groups of Local Fields

Takeshi Saito

Publicado por Cambridge University Press, 2026

ISBN 10: 1009617532 ISBN 13: 9781009617536

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Buch. Condici�n: 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. N� de ref. del art�culo: 9781009617536

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