{ "item_title" : "Ramification Groups of Local Fields", "item_author" : [" Takeshi Saito "], "item_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.", "item_img_path" : "https://covers1.booksamillion.com/covers/bam/1/00/961/753/1009617532_b.jpg", "price_data" : { "retail_price" : "190.00", "online_price" : "190.00", "our_price" : "190.00", "club_price" : "190.00", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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