{"product_id":"triangulated-categories-of-mixed-motives-foundational","title":"Triangulated Categories of Mixed Motives - Foundational","description":"\u003cp\u003eIn this review of Triangulated Categories of Mixed Motives the reviewer finds a rigorous, historically important monograph aimed at researchers and advanced graduate students in algebraic geometry and arithmetic geometry. The single biggest reason to buy is that the book offers the first complete construction of a triangulated category of mixed motives with rational coefficients that satisfies the full Grothendieck six functors formalism, making it an essential reference for anyone working on Beilinson's program or on motivic interpretations of higher Chow groups.\u003c\/p\u003e\u003ch2\u003eKey Features\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eComplete construction:\u003c\/strong\u003e Presents a full construction of a triangulated category of mixed motives with rational coefficients, providing a concrete framework for subsequent research.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eSix functors formalism:\u003c\/strong\u003e Develops the full Grothendieck six functors formalism in the motivic setting, allowing compatibility with standard cohomological tools.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eConnection to Beilinson's program:\u003c\/strong\u003e Explains how rational higher Chow groups are interpreted as extension groups, clarifying important conjectural relationships.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFoundational sources integrated:\u003c\/strong\u003e Builds on Voevodsky's A1-homotopy and motivic complexes while using Gabber's and Ayoub's contributions to ensure technical completeness.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eIntegral coefficient development:\u003c\/strong\u003e Includes a thorough development of motivic complexes with integral coefficients over general bases, useful for work beyond rational coefficients.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch2\u003eWho It's For\u003c\/h2\u003e\u003cp\u003eThis book is primarily for researchers, postdoctoral scholars, and advanced graduate students who are already fluent in homotopical methods and familiar with Voevodsky's A1-homotopy theory and motivic complexes. It is most valuable to those pursuing Beilinson's program, studying mixed motives, or using the six functors formalism in arithmetic geometry.\u003c\/p\u003e\u003cp\u003eThose looking for an introductory text or a gentle entry to motives should look elsewhere, since the monograph assumes significant background in algebraic geometry, etale cohomology and the technical foundations laid out in SGA4 and related work.\u003c\/p\u003e\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eAuthoritative construction that settles key foundational aspects of mixed motives and rational coefficients.\u003c\/li\u003e\n\u003cli\u003eCareful integration of Voevodsky's theories with Gabber's and Ayoub's results for technical robustness.\u003c\/li\u003e\n\u003cli\u003eUseful treatment of motivic complexes with integral coefficients that extends applicability beyond rational cases.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eHighly technical and assumes deep prior knowledge, limiting accessibility to non-specialists.\u003c\/li\u003e\n\u003cli\u003eNot intended as an introductory textbook, so readers seeking pedagogical exposition may find it dense.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch2\u003eSpecifications\u003c\/h2\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eTriangulated Categories of Mixed Motives\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eSpringer Monographs in Mathematics\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthors\u003c\/td\u003e\n\u003ctd\u003eDenis-Charles Cisinski, Frederic Deglise\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eMain aim\u003c\/td\u003e\n\u003ctd\u003eConstruct triangulated category of mixed motives with rational coefficients\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eKey formalisms\u003c\/td\u003e\n\u003ctd\u003eGrothendieck six functors, A1-homotopy, motivic complexes\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAdditional content\u003c\/td\u003e\n\u003ctd\u003eTheory of motivic complexes with integral coefficients over general bases\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\u003ch2\u003eOur Verdict\u003c\/h2\u003e\u003cp\u003eFor specialists in algebraic and arithmetic geometry this monograph is indispensable: it provides a historically significant, technically complete construction of mixed motives that supports ongoing research tied to Beilinson's program. While dense for newcomers, its rigorous treatment and integration of foundational work make it excellent value as a reference and research tool.\u003c\/p\u003e\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003eDoes this book construct mixed motives with rational coefficients?\u003c\/strong\u003e\u003cbr\u003eYes. The book gives a complete construction of a triangulated category of mixed motives with rational coefficients consistent with the six functors formalism.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eIs prior background required to read this monograph?\u003c\/strong\u003e\u003cbr\u003eYes. Readers should be familiar with Voevodsky's A1-homotopy theory, motivic complexes, and foundational materials such as SGA4 to follow the arguments.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eDoes the book address integral coefficients?\u003c\/strong\u003e\u003cbr\u003eIt does: the authors develop the theory of motivic complexes with integral coefficients over general bases alongside the rational theory.\u003c\/p\u003e","brand":"Denis-Charles Cisinski, Frederic Deglise","offers":[{"title":"Default Title","offer_id":48232965800155,"sku":"3030332446","price":129.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/61barzhoefL._SL1254.jpg?v=1770843732","url":"https:\/\/gearmusthave.com\/products\/triangulated-categories-of-mixed-motives-foundational","provider":"GearMustHave","version":"1.0","type":"link"}