Positivity in Arakelov Geometry over Adelic Curves
Hilbert-Samuel Formula and Equidistribution Theorem
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Beschreibung
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.
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.
Provides new results on the arithmetic positivities of Arakelov geometry over adelic curves Highlights connections with several classical topics in Arakelov geometry and Diophantine geometry Includes detailed proofs and explanations
Autor*in
Huayi Chen
Themen in »Positivity in Arakelov Geometry over Adelic Curves«
Arakelov geometry adelic curves Hilbert-Samuel formula adelic line bundle arithmetic intersection positivity conditions Fujita approximation