An arithmetic Riemann-Roch theorem for singular arithmetic surfaces / / Wayne Aitken

• Record Nr.: UNINA9910788759603321
• Autore: Aitken Wayne <1963->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 1996; ©1996
• ISBN: 1-4704-0158-4
• Descrizione fisica: 1 online resource (189 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 120, Number 573
• Disciplina: 512/.74
• Soggetti: Arithmetical algebraic geometry; Riemann-Roch theorems
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "March 1996, volume 120, number 573 (first of 4 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""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""