Ramification groups of local fields : with geometric applications / Takeshi Saito, University of Tokyo.

Format:

Book

Author/Creator:

Sait, Takeshi, 1961- Author.

Series:

New mathematical monographs ; 54.

New mathematical monographs ; 54

Language:

English

Subjects (All):

Local fields (Algebra).

Galois theory.

Valuation theory.

Arithmetical algebraic geometry.

Physical Description:

1 online resource (xix, 452 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge, United Kingdom : Cambridge University Press, 2026.

Summary:

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.

Notes:

Title from publisher's bibliographic system (viewed on 01 Jun 2026).

Description based on publisher supplied metadata and other sources.

ISBN:

1-009-61756-7

9781009617529

OCLC:

1589182621