Progress in Mathematics: Hilbert-Samuel Formula and Equidistribution Theorem

Chen, Huayi; Moriwaki, Atsushi

This monograph presents new research on Arakelov geometry over adelic curves, a novel theory of arithmetic geometry developed by the authors. It explores positivity conditions and establishes the Hilbert-Samuel formula and the equidistribution theorem in the context of adelic curves. Connections with several classical topics in Arakelov geometry and Diophantine geometry are highlighted, such as the arithmetic Hilbert-Samuel formula, positivity of line bundles, equidistribution of small subvarieties, and theorems resembling the Bogomolov conjecture. Detailed proofs and explanations are provided to ensure the text is accessible to both graduate students and experienced researchers.

Details

Published by: Birkhäuser

Publication Date: 2024-08-22

Format: Hardcover

ISBN-13: 9783031616679

DOI: 10.1007/978-3-031-61668-6

Dimensions: 235cm x155cm

Pages: 251