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Arakelov geometry /

Bibliographic Details
Main Author: Moriwaki, Atsushi, 1960- (Author, Translator)
Format: Book
Language:English
Language Notes:In English.
Published: Providence, Rhode Island : American Mathematical Society, 2014.
Edition:English language edition.
Series:Translations of mathematical monographs ; v. 244.
Subjects:
Arakelov theory.
Geometry, Algebraic.
Algebraic geometry > Arithmetic problems. Diophantine geometry > Arithmetic varieties and schemes; Arakelov theory; heights.
Number theory > Arithmetic algebraic geometry (Diophantine geometry) > Heights.
Dynamical systems and ergodic theory > Arithmetic and non-Archimedean dynamical systems > Height functions; Green functions; invariant measures.
Table of Contents:
  • Preliminaries
  • Geometry of numbers
  • Arakelov geometry on arithmetic curves
  • Arakelov geometry on arithmetic surfaces
  • Arakelov geometry on general arithmetic varieties
  • Arithmetic volume function and its continuity
  • Nakai-Moishezon criterion on an arithmetic variety
  • Arithmetic Bogomolov inequality
  • Lang-Bogomolov conjecture.