{"product_id":"ramification-groups-of-local-fields-with-geometric-applications-9781009617536","title":"Ramification Groups of Local Fields: With Geometric Applications","description":"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Takeshi Saito\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Cambridge University Press\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 06\/18\/2026\u003cbr\u003e\u003cb\u003eSeries:\u003c\/b\u003e New Mathematical Monographs #53\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 474\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.76lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 1.06d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9781009617536","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48296569307273,"sku":"9781009617536","price":190.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0636\/9240\/6921\/files\/img_a1d2dad1-084c-4eb2-b8a1-54a6d5564180.jpg?v=1788842936","url":"https:\/\/sonsanddaughtersbooks.com\/products\/ramification-groups-of-local-fields-with-geometric-applications-9781009617536","provider":"Sons and Daughters Books","version":"1.0","type":"link"}