{"product_id":"ramification-groups-of-local-fields-takeshi-saito-9781009617536","title":"Ramification Groups of Local Fields","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\u003eISBN-10:\u003c\/b\u003e 1009617532\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781009617536\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Cambridge University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 06\/18\/2026\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 474\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.76lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 1.06d","brand":"Takeshi Saito","offers":[{"title":"Hardcover","offer_id":48743046611199,"sku":"9781009617536","price":190.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_a3428032-cc9f-4a39-b3c9-32d25f036d04.jpg?v=1782449423","url":"https:\/\/www.whiterainbookhouse.com\/products\/ramification-groups-of-local-fields-takeshi-saito-9781009617536","provider":"WR Book House","version":"1.0","type":"link"}