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This book provides a self-contained proof of the Mordell conjecture (Faltings's theorem) - one of the most important achievements in Diophantine geometry - alongside a concise introduction to the field of Diophantine geometry itself, at a level suitable for advanced undergraduate students and graduate students.

Mathematics, Number theory, Algebra

"A self-contained text providing all the basics of fractional Sobolev spaces. The book provides the background and relevant theory with explanations, alternatives and comparisons, and includes discussion of the Hardy and Rellich inequalities, first in classical format and then in fractional versions. Ideal for researchers and graduate students"--

This book gives the first complete treatment of the moduli theory of varieties of dimension larger than one, aimed at researchers and graduate students in algebraic geometry and related areas. The first chapter provides a historical introduction to the subject, while later chapters provide all necessary background material.