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Positivity in Arakelov Geometry Over Adelic Curves
Huayi ChenAtsushi Moriwaki
其他書名
Hilbert-Samuel Formula and Equidistribution Theorem
出版Springer Nature, 2024
ISBN30316166859783031616686
URLhttp://books.google.com.hk/books?id=IpkbEQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋Zusammenfassung: 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