Introduction to Arakelov Theory

Focusing on advanced arithmetic concepts, this book explores Arakelov's introduction of a component at infinity, leading to global theorems in the arithmetic context of number fields. It covers significant topics like the Hodge Index Theorem, the Arakelov adjunction formula, and the Faltings Riemann-Roch theorem, aimed at second-year graduate students and researchers. Notably, the residue theorem is established using Kunz and Waldi's direct method, and the Faltings theorem is presented without semistability assumptions, ensuring thorough explanations and comprehensive references.