03664nam 22007215 450 991029997800332120200702123643.088-7642-501-210.1007/978-88-7642-501-1(CKB)3710000000212216(Springer)9788876425011(MH)014131723-X(SSID)ssj0001297292(PQKBManifestationID)11779941(PQKBTitleCode)TC0001297292(PQKBWorkID)11363310(PQKB)10373997(DE-He213)978-88-7642-501-1(MiAaPQ)EBC6315260(MiAaPQ)EBC5577103(Au-PeEL)EBL5577103(OCoLC)1066189122(PPN)179923889(EXLCZ)99371000000021221620140701d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierIntroductory Notes on Valuation Rings and Function Fields in One Variable /by Renata Scognamillo, Umberto Zannier1st ed. 2014.Pisa :Scuola Normale Superiore :Imprint: Edizioni della Normale,2014.1 online resource (VIII, 119 p.)online resourceLecture Notes (Scuola Normale Superiore) ;14Bibliographic Level Mode of Issuance: Monograph88-7642-500-4 Generalities on function fields of one variable -- Valuation rings -- Completions -- Appendices on Hilbert's Nullstellensatz, Puiseux series, Dedekind domains.The 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.Lecture Notes (Scuola Normale Superiore) ;14AlgebraGeometryNumber theoryAlgebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11000Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21006Number Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Algebra.Geometry.Number theory.Algebra.Geometry.Number Theory.516.35Scognamillo Renataauthttp://id.loc.gov/vocabulary/relators/aut310294Zannier Umbertoauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299978003321Introductory Notes on Valuation Rings and Function Fields in One Variable2528333UNINAThis 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