LEADER 03664nam 22007215 450 001 9910299978003321 005 20200702123643.0 010 $a88-7642-501-2 024 7 $a10.1007/978-88-7642-501-1 035 $a(CKB)3710000000212216 035 $a(Springer)9788876425011 035 $a(MH)014131723-X 035 $a(SSID)ssj0001297292 035 $a(PQKBManifestationID)11779941 035 $a(PQKBTitleCode)TC0001297292 035 $a(PQKBWorkID)11363310 035 $a(PQKB)10373997 035 $a(DE-He213)978-88-7642-501-1 035 $a(MiAaPQ)EBC6315260 035 $a(MiAaPQ)EBC5577103 035 $a(Au-PeEL)EBL5577103 035 $a(OCoLC)1066189122 035 $a(PPN)179923889 035 $a(EXLCZ)993710000000212216 100 $a20140701d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntroductory Notes on Valuation Rings and Function Fields in One Variable /$fby Renata Scognamillo, Umberto Zannier 205 $a1st ed. 2014. 210 1$aPisa :$cScuola Normale Superiore :$cImprint: Edizioni della Normale,$d2014. 215 $a1 online resource (VIII, 119 p.)$conline resource 225 1 $aLecture Notes (Scuola Normale Superiore) ;$v14 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a88-7642-500-4 327 $aGeneralities on function fields of one variable -- Valuation rings -- Completions -- Appendices on Hilbert's Nullstellensatz, Puiseux series, Dedekind domains. 330 $aThe book deals with the (elementary and introductory) theory of valuation rings. As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory of algebraic curves and their function fields. The correspondences of this with other viewpoints (e.g. of geometrical or topological nature) are often indicated, also to provide motivations and intuition for many results. Links with arithmetic are also often indicated. There are three appendices, concerning Hilbert?s Nullstellensatz (for which several proofs are provided), Puiseux series and Dedekind domains. There are also several exercises, often accompanied by hints, which sometimes develop further results not included in full for brevity reasons. 410 0$aLecture Notes (Scuola Normale Superiore) ;$v14 606 $aAlgebra 606 $aGeometry 606 $aNumber theory 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aAlgebra. 615 0$aGeometry. 615 0$aNumber theory. 615 14$aAlgebra. 615 24$aGeometry. 615 24$aNumber Theory. 676 $a516.35 700 $aScognamillo$b Renata$4aut$4http://id.loc.gov/vocabulary/relators/aut$0310294 702 $aZannier$b Umberto$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299978003321 996 $aIntroductory Notes on Valuation Rings and Function Fields in One Variable$92528333 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress