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Positivity in Arakelov Geometry over Adelic Curves Hilbert-Samuel Formula and Equidistribution Theorem /

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 wit...

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Main Authors: Chen, Huayi (Author), Moriwaki, Atsushi (Author)
Korporativna značnica: SpringerLink (Online service)
Format: Elektronski eKnjiga
Jezik:angleščina
Izdano: Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024.
Izdaja:1st ed. 2024.
Serija:Progress in Mathematics, 355
Teme:
Algebraic geometry.
Number theory.
Algebraic Geometry.
Number Theory.
Online dostop:https://doi.org/10.1007/978-3-031-61668-6
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Kazalo:
  • 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.

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