| Introduction to Arakelov Theory Contributor(s): Lang, Serge (Author) |
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ISBN: 3540967931 ISBN-13: 9783540967934 Publisher: Springer OUR PRICE: $55.58 Product Type: Hardcover - Other Formats Published: December 1988 |
| Additional Information |
| BISAC Categories: - Mathematics | Number Theory - Mathematics | Algebra - General |
| Dewey: 512.72 |
| Physical Information: 8 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |