LEADER 04530nam 22006135 450 001 9910360850903321 005 20200701135218.0 010 $a3-030-33242-X 024 7 $a10.1007/978-3-030-33242-6 035 $a(CKB)4100000009845271 035 $a(DE-He213)978-3-030-33242-6 035 $a(MiAaPQ)EBC5975953 035 $a(PPN)257359540 035 $a(EXLCZ)994100000009845271 100 $a20191109d2019 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTriangulated Categories of Mixed Motives /$fby Denis-Charles Cisinski, Frédéric Déglise 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XLII, 406 p. 1 illus.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 311 $a3-030-33241-1 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Part I Fibred categories and the six functors formalism -- Part II Construction of fibred categories -- Part III Motivic complexes and relative cycles -- Part IV Beilinson motives and algebraic K-theory -- References -- Index -- Notation -- Index of properties of P-fibred triangulated categories. 330 $aThe primary aim of this monograph is to achieve part of Beilinson?s program on mixed motives using Voevodsky?s theories of $\mathbb{A}^1$-homotopy and motivic complexes. Historically, this book is the first to give a complete construction of a triangulated category of mixed motives with rational coefficients satisfying the full Grothendieck six functors formalism as well as fulfilling Beilinson?s program, in particular the interpretation of rational higher Chow groups as extension groups. Apart from Voevodsky?s entire work and Grothendieck?s SGA4, our main sources are Gabber?s work on étale cohomology and Ayoub?s solution to Voevodsky?s cross functors theory. We also thoroughly develop the theory of motivic complexes with integral coefficients over general bases, along the lines of Suslin and Voevodsky. Besides this achievement, this volume provides a complete toolkit for the study of systems of coefficients satisfying Grothendieck? six functors formalism, including Grothendieck-Verdier duality. It gives a systematic account of cohomological descent theory with an emphasis on h-descent. It formalizes morphisms of coefficient systems with a view towards realization functors and comparison results. The latter allows to understand the polymorphic nature of rational mixed motives. They can be characterized by one of the following properties: existence of transfers, universality of rational algebraic K-theory, h-descent, étale descent, orientation theory. This monograph is a longstanding research work of the two authors. The first three parts are written in a self-contained manner and could be accessible to graduate students with a background in algebraic geometry and homotopy theory. It is designed to be a reference work and could also be useful outside motivic homotopy theory. The last part, containing the most innovative results, assumes some knowledge of motivic homotopy theory, although precise statements and references are given. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aAlgebraic geometry 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aK-theory 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aK-Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11086 615 0$aAlgebraic geometry. 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 0$aK-theory. 615 14$aAlgebraic Geometry. 615 24$aCategory Theory, Homological Algebra. 615 24$aK-Theory. 676 $a516.35 700 $aCisinski$b Denis-Charles$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781815 702 $aDéglise$b Frédéric$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910360850903321 996 $aTriangulated Categories of Mixed Motives$92500663 997 $aUNINA