{"product_id":"local-fields-9780387904245","title":"Local Fields","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe goal of this book is to present local class field theory from the cohomo­ logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of \"local\" (i.e., complete for a discrete valuation) fields with finite residue field.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eOne Local Fields (Basic Facts).- I Discrete Valuation Rings and Dedekind Domains.- II Completion.- Two Ramification.- III Discriminant and Different.- IV Ramification Groups.- V The Norm.- VI Artin Representation.- Three Group Cohomology.- VII Basic Facts.- VIII Cohomology of Finite Groups.- IX Theorems of Tate and Nakayama.- X Galois Cohomology.- XI Class Formations.- Four Local Class Field Theory.- XII Brauer Group of a Local Field.- XIII Local Class Field Theory.- XIV Local Symbols and Existence Theorem.- XV Ramification.- Supplementary Bibliography for the English Edition.","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":53733838848343,"sku":"9780387904245","price":999.99,"currency_code":"GBP","in_stock":false}],"url":"https:\/\/bookcurl.com\/products\/local-fields-9780387904245","provider":"Book Curl","version":"1.0","type":"link"}