Introduction to Arakelov Theory

Arakelov introduced a component at infinity in arithmetic considerations thusgiving rise to global theorems similar to those of the theory of surfaces butin an ... » 

Arakelov introduced a component at infinity in arithmetic considerations thusgiving rise to global theorems similar to those of the theory of surfaces butin an arithmetic context over the ring of integers of a number field. The bookgives an introduction to this theory including the analogues of the HodgeIndex Theorem the Arakelov adjunction formula and the Faltings RiemannRochtheorem. The book is intended for second year graduate students and researchersin the field who want a systematic introduction to the subject. The residuetheorem which forms the basis for the adjunction formula is proved by adirect method due to Kunz and Waldi. The Faltings RiemannRoch theorem isproved without assumptions of semistability. An effort has been made to includeall necessary details and as complete references as possible especially toneeded facts of analysis for Greens functions and the Faltings metrics. «