9781009617536 - Ramification Groups of Local Fields: with Geometric Applications (New Mathematical Monographs, Series Number 53) von Saito, Takeshi (3 Ergebnisse)

Zustand: New. 2026. hardcover. . . . . . Books ship from the US and Ireland.

Hardcover. Zustand: Brand New. 478 pages. 6.00x1.06x9.00 inches. In Stock.

Buch. Zustand: 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.