LEADER 03872nam 22005055 450 001 996418258203316 005 20200727172825.0 010 $a3-658-30733-1 024 7 $a10.1007/978-3-658-30733-2 035 $a(CKB)4100000011363609 035 $a(DE-He213)978-3-658-30733-2 035 $a(MiAaPQ)EBC6272555 035 $a(Au-PeEL)EBL6272555 035 $a(OCoLC)1195821249 035 $a(PPN)259391573 035 $a(EXLCZ)994100000011363609 100 $a20200727d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebraic Geometry I: Schemes$b[electronic resource] $eWith Examples and Exercises /$fby Ulrich Görtz, Torsten Wedhorn 205 $a2nd ed. 2020. 210 1$aWiesbaden :$cSpringer Fachmedien Wiesbaden :$cImprint: Springer Spektrum,$d2020. 215 $a1 online resource (VII, 626 p. 15 illus.) 225 1 $aSpringer Studium Mathematik - Master,$x2509-9310 311 $a3-658-30732-3 327 $aIntroduction -- 1 Prevarieties -- 2 Spectrum of a Ring -- 3 Schemes -- 4 Fiber products -- 5 Schemes over fields -- 6 Local Properties of Schemes -- 7 Quasi-coherent modules -- 8 Representable Functors -- 9 Separated morphisms -- 10 Finiteness Conditions -- 11 Vector bundles -- 12 Affine and proper morphisms -- 13 Projective morphisms -- 14 Flat morphisms and dimension -- 15 One-dimensional schemes -- 16 Examples. . 330 $aThis book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get started, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes. For the second edition, several mistakes and many smaller errors and misprints have been corrected. Contents Prevarieties - Spectrum of a Ring - Schemes - Fiber products - Schemes over fields - Local properties of schemes - Quasi-coherent modules - Representable functors - Separated morphisms - Finiteness Conditions - Vector bundles - Affine and proper morphisms - Projective morphisms - Flat morphisms and dimension - One-dimensional schemes - Examples About the Authors Prof. Dr. Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt. 410 0$aSpringer Studium Mathematik - Master,$x2509-9310 606 $aAlgebraic geometry 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aAlgebraic geometry. 615 14$aAlgebraic Geometry. 676 $a516.35 700 $aGörtz$b Ulrich$4aut$4http://id.loc.gov/vocabulary/relators/aut$0760547 702 $aWedhorn$b Torsten$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418258203316 996 $aAlgebraic Geometry I: Schemes$91886619 997 $aUNISA