LEADER 03992nam 22005295 450 001 9910768461203321 005 20240703110340.0 010 $a3-658-43031-1 024 7 $a10.1007/978-3-658-43031-3 035 $a(MiAaPQ)EBC30965490 035 $a(Au-PeEL)EBL30965490 035 $a(OCoLC)1410592494 035 $a(DE-He213)978-3-658-43031-3 035 $a(CKB)29026943700041 035 $a(EXLCZ)9929026943700041 100 $a20231122d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebraic Geometry II: Cohomology of Schemes $eWith Examples and Exercises /$fby Ulrich Görtz, Torsten Wedhorn 205 $a1st ed. 2023. 210 1$aWiesbaden :$cSpringer Fachmedien Wiesbaden :$cImprint: Springer Spektrum,$d2023. 215 $a1 online resource (877 pages) 225 1 $aSpringer Studium Mathematik - Master,$x2509-9329 311 08$aPrint version: Görtz, Ulrich Algebraic Geometry II: Cohomology of Schemes Wiesbaden : Springer Fachmedien Wiesbaden GmbH,c2023 327 $aIntroduction -- 17 Differentials -- 18 Étale and smooth morphisms -- 19 Local complete intersections -- 20 The étale topology -- 21 Cohomology of sheaves of modules -- 22 Cohomology of quasi-coherent modules -- 23 Cohomology of projective and proper schemes -- 24 Theorem on formal functions -- 25 Duality -- 26 Curves -- 27 Abelian schemes -- F Homological algebra -- G Commutative algebra II. 330 $aThis book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously. The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results. Contents Differentials - Étale and smooth morphisms - Local complete intersections - The étale topology - Cohomology of sheaves of modules - Cohomology of quasi-coherent sheaves - Cohomology of projective and proper schemes - Theorem on formal functions - Duality - Curves - Abelian schemes - Appendix: Homological Algebra - Appendix: Commutative Algebra About the Authors Prof. Dr. Ulrich Görtz, Department of Mathematics, University of Duisburg-Essen Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt. 410 0$aSpringer Studium Mathematik - Master,$x2509-9329 606 $aGeometry, Algebraic 606 $aAlgebraic Geometry 606 $aGeometria algebraica$2thub 608 $aLlibres electrňnics$2thub 615 0$aGeometry, Algebraic. 615 14$aAlgebraic Geometry. 615 7$aGeometria algebraica 676 $a516.35 700 $aGörtz$b Ulrich$0760547 701 $aWedhorn$b Torsten$0755965 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910768461203321 996 $aAlgebraic Geometry II: Cohomology of Schemes$93657066 997 $aUNINA