Adelic Line Bundles on Quasi-Projective Varieties (eBook)

Xinyi Yuan, Shou-wu Zhang (Autoren)

eBook Download: PDF

2026
283 Seiten
Princeton University Press (Verlag)
978-0-691-27870-4 (ISBN)

Infos

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

Produkt-Details

• Erscheint lt. Verlag: 13.1.2026
• Reihe/Serie: Annals of Mathematics Studies
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Schlagworte: Adelic • adelic curves • adelic line bundles • adelic metrics • Algebraic Geometry • algebraic points • ample line bundles • analytic spaces • Arakelov Theory • arithmetic • arithmetic compactifications • Arithmetic Geometry • arithmetic intersection numbers • arithmetic setting • asymptotic behavior • birational invariants • boundary • boundary topology • Canonical • canonical heights • characteristic zero • compactified varieties • Deligne pairing • Diophantine properties • Divisor • Dynamical properties • effective sections • Equidistribution theorem • Finitely • finitely generated fields • Function Fields • Galois orbits • geometric setting • graded linear series • height functions • Hermitian • Hermitian line bundles • Hilbert-Samuel formula • integrable adelic line bundles • Integral scheme • Intersection theory • isomorphism • limit processes • line bundle • metric • metrized line bundles • minimal slopes • model adelic line bundles • moduli spaces • Morphism • Nakai-Moishezon theorem • nef adelic line bundles • Néron-Tate heights • Number Fields • Number Theory • numerical properties • Positivity • positivity conditions • PROJECTIVE • projective compactifications • proper models • quasi • quasi-projective varieties • Rational • semipositive line bundles • slope boundedness • small points • Theorem • variety • Volumes
• ISBN-10: 0-691-27870-9 / 0691278709
• ISBN-13: 978-0-691-27870-4 / 9780691278704