LEADER 03757nam 22006615 450 001 9910438150003321 005 20200630165014.0 010 $a1-4471-4829-0 024 7 $a10.1007/978-1-4471-4829-6 035 $a(CKB)3400000000088935 035 $a(EBL)1156141 035 $a(OCoLC)831115598 035 $a(SSID)ssj0000851048 035 $a(PQKBManifestationID)11509946 035 $a(PQKBTitleCode)TC0000851048 035 $a(PQKBWorkID)10838634 035 $a(PQKB)10291374 035 $a(DE-He213)978-1-4471-4829-6 035 $a(MiAaPQ)EBC1156141 035 $a(MiAaPQ)EBC6315836 035 $a(PPN)16829432X 035 $a(EXLCZ)993400000000088935 100 $a20121116d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAlgebraic Geometry and Commutative Algebra /$fby Siegfried Bosch 205 $a1st ed. 2013. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2013. 215 $a1 online resource (514 p.) 225 1 $aUniversitext,$x0172-5939 300 $aDescription based upon print version of record. 311 $a1-4471-4828-2 320 $aIncludes bibliographical references and index. 327 $aRings and Modules -- The Theory of Noetherian Rings -- Integral Extensions -- Extension of Coefficients and Descent -- Homological Methods: Ext and Tor -- Affine Schemes and Basic Constructions -- Techniques of Global Schemes -- Etale and Smooth Morphisms -- Projective Schemes and Proper Morphisms. 330 $aAlgebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck?s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved the way to spectacular progress such as the proof of Fermat?s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broaden their view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature. 410 0$aUniversitext,$x0172-5939 606 $aAlgebraic geometry 606 $aCommutative algebra 606 $aCommutative rings 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 615 0$aAlgebraic geometry. 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 14$aAlgebraic Geometry. 615 24$aCommutative Rings and Algebras. 676 $a516.35 700 $aBosch$b Siegfried$4aut$4http://id.loc.gov/vocabulary/relators/aut$041946 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438150003321 996 $aAlgebraic geometry and commutative algebra$9837691 997 $aUNINA