{"product_id":"etale-cohomology-theory-in-depth-mathematical-lei","title":"Etale Cohomology Theory - In-depth Mathematical Lei","description":"\u003cp\u003eOur review of Etale Cohomology Theory finds it to be a concentrated, advanced text aimed at graduate students and researchers who need a coherent exposition of the SGA developments on etale cohomology. The single biggest reason to buy is its systematic coverage of material from SGA 1, SGA 4, SGA 4 1\/2 and SGA 5, collected here to provide a working reference for topics such as the etale fundamental group, l-adic cohomology and duality, rather than an introductory textbook.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eComprehensive SGA coverage:\u003c\/strong\u003e Brings together the main results from SGA 1, SGA 4, SGA 4 1\/2 and SGA 5 so readers can consult related theorems and proofs in one volume.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eEtale fundamental groups and Galois cohomology:\u003c\/strong\u003e Treats fundamental groups and Galois cohomology in a way that clarifies their interaction for arithmetic geometry applications.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eDerived categories and base change:\u003c\/strong\u003e Includes the necessary derived category language and base change theorems that are essential for modern uses of etale cohomology.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eDuality and l-adic theory:\u003c\/strong\u003e Presents duality statements and l-adic cohomology material that researchers will reference in advanced work.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003ePrerequisite guidance:\u003c\/strong\u003e Assumes basic algebraic geometry and advanced commutative algebra so motivated readers know the expected background before starting.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eEtale Cohomology Theory is best suited to graduate students preparing for research in arithmetic geometry and to active researchers who need a focused, rigorous exposition of SGA material without chasing the original seminar notes. Its strength is as a reference and as a consolidation of scattered seminar results into a readable sequence.\u003c\/p\u003e\n\u003cp\u003eReaders looking for an elementary introduction or a gentle first course in cohomology should look elsewhere, since the book presumes solid background in algebraic geometry and commutative algebra rather than building foundations from scratch.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eCareful assembly of core SGA topics provides a single reference for etale cohomology results.\u003c\/li\u003e\n\u003cli\u003eClear presentation of the relation between fundamental groups, Galois cohomology and l-adic methods helps in research applications.\u003c\/li\u003e\n\u003cli\u003eIncludes derived category language and base change theorems that are practically useful for advanced users.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe book requires prior study of algebraic geometry and advanced commutative algebra, so it is not suitable as an introductory text.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eEtale Cohomology Theory (Nankai Tracts in Mathematics)\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor\u003c\/td\u003e\n\u003ctd\u003eLei Fu\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSubject focus\u003c\/td\u003e\n\u003ctd\u003eEtale cohomology, fundamental groups, Galois cohomology, l-adic cohomology\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSource material\u003c\/td\u003e\n\u003ctd\u003eBased on SGA 1, SGA 4, SGA 4 1\/2 and SGA 5\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIntended readers\u003c\/td\u003e\n\u003ctd\u003eGraduate students and researchers in arithmetic geometry\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePrerequisites\u003c\/td\u003e\n\u003ctd\u003eBasic algebraic geometry and advanced commutative algebra\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eEtale Cohomology Theory is a valuable, compact reference for anyone who already knows algebraic geometry and needs a coherent presentation of SGA material on etale cohomology. It is well worth acquiring for graduate students moving into research and for researchers seeking a consolidated source of proofs and statements on fundamental groups, duality and l-adic methods.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eIs this book suitable for beginners?\u003c\/strong\u003e\u003cbr\u003eNo. The text expects background in basic algebraic geometry and advanced commutative algebra, so beginners should consult introductory cohomology texts first.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes it cover l-adic cohomology?\u003c\/strong\u003e\u003cbr\u003eYes. The book includes material on l-adic cohomology alongside duality and base change theorems drawn from the SGA seminars.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eWill it serve as a research reference?\u003c\/strong\u003e\u003cbr\u003eYes. Its consolidation of SGA 1, SGA 4, SGA 4 1\/2 and SGA 5 makes it useful as a reference for researchers in arithmetic geometry.\u003c\/p\u003e","brand":"Lei Fu","offers":[{"title":"Default Title","offer_id":48638894112987,"sku":"B007N3FBKG","price":153.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/41W2XBpDzjL.jpg?v=1778733676","url":"https:\/\/gearmusthave.com\/products\/etale-cohomology-theory-in-depth-mathematical-lei","provider":"GearMustHave","version":"1.0","type":"link"}