LEADER 07017nam 22017895 450 001 9910154744803321 005 20190708092533.0 010 $a1-4008-8149-8 024 7 $a10.1515/9781400881499 035 $a(CKB)3710000000631343 035 $a(SSID)ssj0001651272 035 $a(PQKBManifestationID)16426197 035 $a(PQKBTitleCode)TC0001651272 035 $a(PQKBWorkID)13976268 035 $a(PQKB)10755492 035 $a(MiAaPQ)EBC4738514 035 $a(DE-B1597)467991 035 $a(OCoLC)979882335 035 $a(DE-B1597)9781400881499 035 $a(EXLCZ)993710000000631343 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aEtale Homotopy of Simplicial Schemes. (AM-104), Volume 104 /$fEric M. Friedlander 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$d©1983 215 $a1 online resource (193 pages) 225 0 $aAnnals of Mathematics Studies ;$v231 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-691-08317-7 311 $a0-691-08288-X 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tINTRODUCTION -- $t1. ETALE SITE OF A SIMPLICIAL SCHEME -- $t2. SHEAVES AND COHOMOLOGY -- $t3. COHOMOLOGY VIA HYPERCOVERINGS -- $t4. ETALE TOPOLOGICAL TYPE -- $t5. HOMOTOPY INVARIANTS -- $t6. WEAK EQUIVALENCES, COMPLETIONS, AND HOMOTOPY LIMITS -- $t7. FINITENESS AND HOMOLOGY -- $t8. COMPARISON OF HOMOTOPY TYPES -- $t9. APPLICATIONS TO TOPOLOGY -- $t10. COMPARISON OF GEOMETRIC AND HOMOTOPY THEORETIC FIBRES -- $t11. APPLICATIONS TO GEOMETRY -- $t12. APPLICATIONS TO FINITE CHE VALLEY GROUPS -- $t13. FUNCTION COMPLEXES -- $t14. RELATIVE COHOMOLOGY -- $t15. TUBULAR NEIGHBORHOODS -- $t16. GENERALIZED COHOMOLOGY -- $t17. POINCARÉ DUALITY AND LOCALLY COMPACT HOMOLOGY -- $tREFERENCES -- $tINDEX -- $tBackmatter 330 $aThis book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander presents many of his own applications of this theory to algebraic topology, finite Chevalley groups, and algebraic geometry. Of particular interest are the discussions concerning the Adams Conjecture, K-theories of finite fields, and Poincare duality. Because these applications have required repeated modifications of the original formulation of etale homotopy theory, the author provides a new treatment of the foundations which is more general and more precise than previous versions.One purpose of this book is to offer the basic techniques and results of etale homotopy theory to topologists and algebraic geometers who may then apply the theory in their own work. With a view to such future applications, the author has introduced a number of new constructions (function complexes, relative homology and cohomology, generalized cohomology) which have immediately proved applicable to algebraic K-theory. 410 0$aAnnals of mathematics studies ;$vNumber 104. 606 $aHomotopy theory 606 $aSchemes (Algebraic geometry) 606 $aHomology theory 610 $aAbelian group. 610 $aAdams operation. 610 $aAdjoint functors. 610 $aAlexander Grothendieck. 610 $aAlgebraic K-theory. 610 $aAlgebraic closure. 610 $aAlgebraic geometry. 610 $aAlgebraic group. 610 $aAlgebraic number theory. 610 $aAlgebraic structure. 610 $aAlgebraic topology (object). 610 $aAlgebraic topology. 610 $aAlgebraic variety. 610 $aAlgebraically closed field. 610 $aAutomorphism. 610 $aBase change. 610 $aCap product. 610 $aCartesian product. 610 $aClosed immersion. 610 $aCodimension. 610 $aCoefficient. 610 $aCohomology. 610 $aComparison theorem. 610 $aComplex number. 610 $aComplex vector bundle. 610 $aConnected component (graph theory). 610 $aConnected space. 610 $aCoprime integers. 610 $aCorollary. 610 $aCovering space. 610 $aDerived functor. 610 $aDimension (vector space). 610 $aDisjoint union. 610 $aEmbedding. 610 $aExistence theorem. 610 $aExt functor. 610 $aExterior algebra. 610 $aFiber bundle. 610 $aFibration. 610 $aFinite field. 610 $aFinite group. 610 $aFree group. 610 $aFunctor. 610 $aFundamental group. 610 $aGalois cohomology. 610 $aGalois extension. 610 $aGeometry. 610 $aGrothendieck topology. 610 $aHomogeneous space. 610 $aHomological algebra. 610 $aHomology (mathematics). 610 $aHomomorphism. 610 $aHomotopy category. 610 $aHomotopy group. 610 $aHomotopy. 610 $aIntegral domain. 610 $aIntersection (set theory). 610 $aInverse limit. 610 $aInverse system. 610 $aK-theory. 610 $aLeray spectral sequence. 610 $aLie group. 610 $aLocal ring. 610 $aMapping cylinder. 610 $aNatural number. 610 $aNatural transformation. 610 $aNeighbourhood (mathematics). 610 $aNewton polynomial. 610 $aNoetherian ring. 610 $aOpen set. 610 $aOpposite category. 610 $aPointed set. 610 $aPresheaf (category theory). 610 $aReductive group. 610 $aRegular local ring. 610 $aRelative homology. 610 $aResidue field. 610 $aRiemann surface. 610 $aRoot of unity. 610 $aSerre spectral sequence. 610 $aShape theory (mathematics). 610 $aSheaf (mathematics). 610 $aSheaf cohomology. 610 $aSheaf of spectra. 610 $aSimplex. 610 $aSimplicial set. 610 $aSpecial case. 610 $aSpectral sequence. 610 $aSurjective function. 610 $aTheorem. 610 $aTopological K-theory. 610 $aTopological space. 610 $aTopology. 610 $aTubular neighborhood. 610 $aVector bundle. 610 $aWeak equivalence (homotopy theory). 610 $aWeil conjectures. 610 $aWeyl group. 610 $aWitt vector. 610 $aZariski topology. 615 0$aHomotopy theory. 615 0$aSchemes (Algebraic geometry) 615 0$aHomology theory. 676 $a514/.24 700 $aFriedlander$b Eric M., $055737 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154744803321 996 $aEtale Homotopy of Simplicial Schemes. (AM-104), Volume 104$92786625 997 $aUNINA