03057nam a22005295i 4500 978-3-031-61668-6 DE-He213 20251030112911.0 cr nn 008mamaa 240822s2024 sz | s |||| 0|eng d 9783031616686 978-3-031-61668-6 10.1007/978-3-031-61668-6 doi QA564-609 PBMW bicssc MAT012010 bisacsh PBMW thema Chen, Huayi. author. aut http://id.loc.gov/vocabulary/relators/aut 82872 Positivity in Arakelov Geometry over Adelic Curves [electronic resource] : Hilbert-Samuel Formula and Equidistribution Theorem / by Huayi Chen, Atsushi Moriwaki. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024. VIII, 251 p. 7 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Progress in Mathematics, 2296-505X ; 355 Introduction -- Review and Preliminaries -- Normed Graded Linear Series over a Trivially Valued Field -- Arithmetic Volumes over a General Adelic Curve -- Hilbert-Samuel Property -- Relative Ampleness and Nefness -- Global Adelic Space of an Arithmetic Variety -- Generically Big and Pseudo-effective Adelic Line Bundles -- Global Positivity Conditions -- Appendix A: Some Slope Estimates. 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. Algebraic geometry. Number theory. Algebraic Geometry. Number Theory. Moriwaki, Atsushi. author. aut http://id.loc.gov/vocabulary/relators/aut 82873 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031616679 Printed edition: 9783031616693 Printed edition: 9783031616709 Progress in Mathematics, 2296-505X ; 355 74786 https://doi.org/10.1007/978-3-031-61668-6 ZDB-2-SMA ZDB-2-SXMS 62727 62727