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Introduction to Arakelov Theory (Hardcover, 1988 ed.)
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Introduction to Arakelov Theory (Hardcover, 1988 ed.)
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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.
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