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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Adelic Line Bundles on Quasi-Projective Varieties

Adelic Line Bundles on Quasi-Projective Varieties

Zhang, Shou-Wu
Yuan, Xinyi

Paperback

Series: Annals of Mathematics Studies, Book 221

AlgebraGeneral Mathematics

ISBN10: 0691271739
ISBN13: 9780691271736
Publisher: Princeton University Press
Published: Jan 13 2026
Pages: 280
Weight: 0.88
Height: 0.60 Width: 6.14 Depth: 9.21
Language: English

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fields

This book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in both geometric and arithmetic contexts. In the geometric setting, adelic line bundles are defined as limits of line bundles on projective compactifications under the boundary topology. In the arithmetic setting, they are defined as limits of Hermitian line bundles on projective arithmetic compactifications, also under the boundary topology. After establishing these foundational definitions, the book uses the theory to explore key concepts such as intersection theory, effective sections, volumes, and positivity of adelic line bundles. It also applies these results to study height functions of algebraic points and prove an equidistribution theorem on quasi-projective varieties. This theory has broad applications in the study of numerical, dynamical, and Diophantine properties of moduli spaces, quasi-projective varieties, and varieties over finitely generated fields.

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