LEADER 05426nam 22006015 450 001 9910484688503321 005 20200707150121.0 010 $a981-15-1588-3 024 7 $a10.1007/978-981-15-1588-0 035 $a(CKB)4100000010673937 035 $a(DE-He213)978-981-15-1588-0 035 $a(MiAaPQ)EBC6142247 035 $a(PPN)243226756 035 $a(EXLCZ)994100000010673937 100 $a20200318d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBousfield Classes and Ohkawa's Theorem$b[electronic resource] $eNagoya, Japan, August 28-30, 2015 /$fedited by Takeo Ohsawa, Norihiko Minami 205 $a1st ed. 2020. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2020. 215 $a1 online resource (X, 435 p. 9 illus., 1 illus. in color.) 225 1 $aSpringer Proceedings in Mathematics & Statistics,$x2194-1009 ;$v309 311 $a981-15-1587-5 327 $aA.K. Bousfield, Foreword -- Takao Matumoto, Memories on Ohkawa?s mathematical life in Hiroshima -- Carles Casacuberta, Depth and simplicity of Ohkawa?s argument -- Shane Kelly, Some observations about motivic tensor triangulated geometry over a finite field -- Ruth Joachimi, Thick ideals in equivariant and motivic stable homotopy categories -- Takeo Ohsawa, Role of the L2 Method in the study of analytic Families -- Carles Casacuberta and Jiri Rosicky, Combinatorial homotopy categories -- Mark Behrens and Charles Rezk, Spectral algebra models of unstable vn-periodic homotopy theory -- Takeshi Torii, On quasi-categories of comodules and Landweber exactness -- Takuo Matsuoka, Koszul duality for En-algebras in a filtered category -- Takuo Matsuoka, Some technical aspects of factorization algebras on manifolds -- Ryo Kato, Hiroki Okajima and Katsumi Shimomura, Notes on an alegebraic stable homotopy category -- Jack Morava, Operations on integral lifts of K(n) -- Tobias Barthel, A short introduction to the telescope and chromatic splitting conjectures -- Norihiko Minami, From Ohkawa to strong generation via approximable triangulated categories - a variation on the theme of Amnon Neeman's Nagoya lecture series. 330 $aThis volume originated in the workshop held at Nagoya University, August 28?30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins?Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors. 410 0$aSpringer Proceedings in Mathematics & Statistics,$x2194-1009 ;$v309 606 $aAlgebraic topology 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aFunctions of complex variables 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198 615 0$aAlgebraic topology. 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 0$aFunctions of complex variables. 615 14$aAlgebraic Topology. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aSeveral Complex Variables and Analytic Spaces. 676 $a514.24 702 $aOhsawa$b Takeo$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aMinami$b Norihiko$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484688503321 996 $aBousfield Classes and Ohkawa's Theorem$92004327 997 $aUNINA