Positivity in Arakelov geometry over Adelic curves : Hilbert-Samuel formula and equidistribution theorem / Huayi Chen, Atsushi Moriwaki.

Format:

Book

Author/Creator:

Chen, Huayi, author.

Moriwaki, Atsushi, 1960- author.

Series:

Progress in mathematics (Boston, Mass.) ; v. 355.

Progress in mathematics ; v. 355

Language:

English

Subjects (All):

Arakelov theory.

Physical Description:

vii, 253 pages ; 25 cm.

Place of Publication:

Cham : Birkhäuser, 2024

Summary:

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.

Contents:

Introduction

Review and Preliminaries

Normed Graded Linear Series over a Trivially Valued Field

Arithmetic Volumes over a General Adelic Curve

Hilbert-Samuel Property

Relative Ampleness and Nefness

Global Adelic Space of an Arithmetic Variety

Generically Big and Pseudo-effective Adelic Line Bundles

Global Positivity Conditions

Appendix A: Some Slope Estimates.

Notes:

Includes bibliographical references (pages 243-247) and indexes.

Other Format:

Online version: Chen, Huayi. Positivity in Arakelov geometry over Adelic curves.

ISBN:

3031616677

9783031616679

OCLC:

1431177802