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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| Autori principali: | , |
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| Ente Autore: | |
| Natura: | Elettronico eBook |
| Lingua: | inglese |
| Pubblicazione: |
Cham :
Springer Nature Switzerland : Imprint: Birkhäuser,
2024.
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| Edizione: | 1st ed. 2024. |
| Serie: | Progress in Mathematics,
355 |
| Soggetti: | |
| Accesso online: | https://doi.org/10.1007/978-3-031-61668-6 |
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| Riassunto: | 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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| Descrizione fisica: | VIII, 251 p. 7 illus. online resource. |
| ISBN: | 9783031616686 |
| ISSN: | 2296-505X ; |
| DOI: | 10.1007/978-3-031-61668-6 |