Introduction to Arakelov Theory
(Sprache: Englisch)
Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context over the ring of integers of a number field. The book gives an...
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Klappentext zu „Introduction to Arakelov Theory “
Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context over the ring of integers of a number field. The book gives an introduction to this theory, including the analogues of the Hodge Index Theorem, the Arakelov adjunction formula, and the Faltings Riemann-Roch theorem. The book is intended for second year graduate students and researchers in the field who want a systematic introduction to the subject. The residue theorem, which forms the basis for the adjunction formula, is proved by a direct method due to Kunz and Waldi. The Faltings Riemann-Roch theorem is proved without assumptions of semistability. An effort has been made to include all necessary details, and as complete references as possible, especially to needed facts of analysis for Green's functions and the Faltings metrics.
Inhaltsverzeichnis zu „Introduction to Arakelov Theory “
- Foreword- Metrics and Chern Forms
- Green's Functions on Riemann Surfaces
- Intersections on an Arithmetic Surface
- Hodge Index Theorem and the Adjunction Formula
- The Faltings Riemann-Roch Theorem
- Faltings Volumes on Cohomology
- Diophantine Inequalities and Arakelov Theory
- References
- Freqently Used Symbols
- Index
Bibliographische Angaben
- Autor: Serge Lang
- 1988, 187 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 0387967931
- ISBN-13: 9780387967936
- Erscheinungsdatum: 09.11.1988
Sprache:
Englisch
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