03422nam 2200565 450 991082787520332120170816143334.01-4704-0158-4(CKB)3360000000464757(EBL)3113880(SSID)ssj0000888774(PQKBManifestationID)11487560(PQKBTitleCode)TC0000888774(PQKBWorkID)10866809(PQKB)11704252(MiAaPQ)EBC3113880(RPAM)1618215(PPN)195414551(EXLCZ)99336000000046475720140905h19961996 uy 0engur|n|---|||||txtccrAn arithmetic Riemann-Roch theorem for singular arithmetic surfaces /Wayne AitkenProvidence, Rhode Island :American Mathematical Society,1996.©19961 online resource (189 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 120, Number 573"March 1996, volume 120, number 573 (first of 4 numbers)."0-8218-0407-3 Includes bibliographical references.""Contents""; ""Chapter 1. The Intersection Pairing for One-Dimensional Schemes""; ""1. Preliminaries""; ""2. The Determinant of Cohomology Functor""; ""3. The Norm Functor for Zero-Dimensional Schemes""; ""4. The Definition of the Intersection Pairing""; ""5. The Intersection Pairing and Norms""; ""6. The Norm Functor for Divisors""; ""7. Other Properties of the Intersection Pairing""; ""8. Extensions of the Base Field""; ""Chapter 2. The Intersection Pairing for Families of One-dimensional Schemes""; ""1. Introduction""; ""2. Horizontal Divisors""; ""3. The Norm Functor""""4. The Intersection Pairing""""5. The Determinant of Cohomology Line Bundle""; ""6. Flat Base Change""; ""Chapter 3. The Riemann-Roch Isomorphism""; ""1. The Relative Dualizing Sheaf""; ""2. The Adjunction Formula""; ""3. The Duality Isomorphism on Determinants""; ""4. The Riemann-Roch Isomorphism""; ""Chapter 4. Intersection Functions on Complex Curves""; ""1. Motivation: The Non-Archimedean Situation""; ""2. The Archimedean Case: Basic Definitions""; ""3. Intersection Functions on Nonsingular Curves""; ""4. Intersection Functions on Singular Curves: The Existence Theorem""""5. Classification of Intersection Functions: Preliminaries""""6. Classification of Intersection Functions""; ""7. Chern Forms of Intersection Functions""; ""8. Chern Forms of Intersection Functions: Proofs""; ""9. Chern Forms of Intersection Functions: Another Interpretation""; ""Chapter 5. The Arithmetic Riemann-Roch Isomorphism""; ""1. Norms for Determinants of Cohomology""; ""2. The Riemann-Roch Isomorphism for Arithmetic Surfaces""; ""Bibliography""Memoirs of the American Mathematical Society ;Volume 120, Number 573.Arithmetical algebraic geometryRiemann-Roch theoremsArithmetical algebraic geometry.Riemann-Roch theorems.512/.74Aitken Wayne1963-1606333MiAaPQMiAaPQMiAaPQBOOK9910827875203321An arithmetic Riemann-Roch theorem for singular arithmetic surfaces3932083UNINA