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001 978-3-031-61668-6
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020 _a9783031616686
_9978-3-031-61668-6
024 7 _a10.1007/978-3-031-61668-6
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
100 1 _aChen, Huayi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_982872
245 1 0 _aPositivity in Arakelov Geometry over Adelic Curves
_h[electronic resource] :
_bHilbert-Samuel Formula and Equidistribution Theorem /
_cby Huayi Chen, Atsushi Moriwaki.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Birkhäuser,
_c2024.
300 _aVIII, 251 p. 7 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics,
_x2296-505X ;
_v355
505 0 _aIntroduction -- 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.
520 _aThis 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.
650 0 _aAlgebraic geometry.
650 0 _aNumber theory.
650 1 4 _aAlgebraic Geometry.
650 2 4 _aNumber Theory.
700 1 _aMoriwaki, Atsushi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_982873
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031616679
776 0 8 _iPrinted edition:
_z9783031616693
776 0 8 _iPrinted edition:
_z9783031616709
830 0 _aProgress in Mathematics,
_x2296-505X ;
_v355
_974786
856 4 0 _uhttps://doi.org/10.1007/978-3-031-61668-6
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c62727
_d62727