Positivity in Arakelov Geometry over Adelic Curves : Hilbert-Samuel Formula and Equidistribution Theorem
2024 ed.
Book Details
Format
Hardback or Cased Book
Book Series
Progress in Mathematics
ISBN-10
3031616677
ISBN-13
9783031616679
Edition
2024 ed.
Publisher
Birkhauser Verlag AG
Imprint
Birkhauser Verlag AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Aug 22nd, 2024
Print length
251 Pages
Product Classification:
Number theoryAlgebraic geometry
Ksh 23,400.00
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This monograph presents new research on Arakelov geometry over adelic curves, a novel theory of arithmetic geometry developed by the authors.
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.
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