LEADER 04152nam 22006855 450 001 9910299788003321 005 20200630103929.0 010 $a1-4939-2300-5 024 7 $a10.1007/978-1-4939-2300-7 035 $a(CKB)3710000000416757 035 $a(EBL)2096705 035 $a(SSID)ssj0001501579 035 $a(PQKBManifestationID)11896732 035 $a(PQKBTitleCode)TC0001501579 035 $a(PQKBWorkID)11446470 035 $a(PQKB)10006713 035 $a(DE-He213)978-1-4939-2300-7 035 $a(MiAaPQ)EBC2096705 035 $a(PPN)186030169 035 $a(EXLCZ)993710000000416757 100 $a20150527d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLocal Homotopy Theory /$fby John F. Jardine 205 $a1st ed. 2015. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2015. 215 $a1 online resource (508 p.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 300 $aDescription based upon print version of record. 311 $a1-4939-2299-8 320 $aIncludes bibliographical referencesa and index. 327 $aPreface -- 1 Introduction -- Part I Preliminaries -- 2 Homotopy theory of simplicial sets -- 3 Some topos theory -- Part II Simplicial presheaves and simplicial sheaves -- 4 Local weak equivalences -- 5 Local model structures -- 6 Cocycles -- 7 Localization theories -- Part III Sheaf cohomology theory -- 8 Homology sheaves and cohomology groups -- 9 Non-abelian cohomology -- Part IV Stable homotopy theory -- 10 Spectra and T-spectra -- 11 Symmetric T-spectra -- References -- Index. 330 $aThis monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory. Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy theory. A detailed treatment of the formalism of the subject is interwoven with explanations of the motivation, development, and nuances of ideas and results. The coherence of the abstract theory is elucidated through the use of widely applicable tools, such as Barr's theorem on Boolean localization, model structures on the category of simplicial presheaves on a site, and cocycle categories. A wealth of concrete examples convey the vitality and importance of the subject in topology, number theory, algebraic geometry, and algebraic K-theory. Assuming basic knowledge of algebraic geometry and homotopy theory, Local Homotopy Theory will appeal to researchers and advanced graduate students seeking to understand and advance the applications of homotopy theory in multiple areas of mathematics and the mathematical sciences. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aK-theory 606 $aAlgebraic topology 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 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 0$aK-theory. 615 0$aAlgebraic topology. 615 14$aCategory Theory, Homological Algebra. 615 24$aK-Theory. 615 24$aAlgebraic Topology. 676 $a514.24 700 $aJardine$b John F$4aut$4http://id.loc.gov/vocabulary/relators/aut$062267 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299788003321 996 $aLocal homotopy theory$91522428 997 $aUNINA