國立高雄大學圖資館 |

登入

回首頁

Positivity in Arakelov geometry over Adelic curvesHilbert-Samuel formula and equidistribution theorem /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Positivity in Arakelov geometry over Adelic curvesby Huayi Chen, Atsushi Moriwaki.
其他題名:	Hilbert-Samuel formula and equidistribution theorem /
作者:	Chen, Huayi.
其他作者:	Moriwaki, Atsushi.
出版者:	Cham :Springer Nature Switzerland :2024.
面頁冊數:	viii, 251 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Arakelov theory.
電子資源:	https://doi.org/10.1007/978-3-031-61668-6
ISBN:	9783031616686$q(electronic bk.)

Positivity in Arakelov geometry over Adelic curvesHilbert-Samuel formula and equidistribution theorem /
Chen, Huayi.

Positivity in Arakelov geometry over Adelic curvesHilbert-Samuel formula and equidistribution theorem /[electronic resource] :by Huayi Chen, Atsushi Moriwaki. - Cham :Springer Nature Switzerland :2024. - viii, 251 p. :ill., digital ;24 cm. - Progress in mathematics,v. 3552296-505X ;. - Progress in mathematics ;v.295..

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.

ISBN: 9783031616686$q(electronic bk.)

Standard No.: 10.1007/978-3-031-61668-6doiSubjects--Topical Terms:

861059
Arakelov theory.

LC Class. No.: QA242.6

Dewey Class. No.: 516.35

Positivity in Arakelov geometry over Adelic curvesHilbert-Samuel formula and equidistribution theorem /
LDR:02216nmm a22003495a 4500 001 668151
003 DE-He213
005 20240822130250.0
006 m d
007 cr nn 008maaau
008 250107s2024 sz s 0 eng d
020 $a 9783031616686$q(electronic bk.)
020 $a 9783031616679$q(paper)
024 7 $a 10.1007/978-3-031-61668-6 $2 doi
035 $a 978-3-031-61668-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA242.6
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.35 $2 23
090 $a QA242.6 $b .C518 2024
100 1 $a Chen, Huayi. $3 861057
245 1 0 $a Positivity in Arakelov geometry over Adelic curves $h [electronic resource] : $b Hilbert-Samuel formula and equidistribution theorem / $c by Huayi Chen, Atsushi Moriwaki.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Birkhäuser, $c 2024.
300 $a viii, 251 p. : $b ill., digital ; $c 24 cm.
347 $a text file $b PDF $2 rda
490 1 $a Progress in mathematics, $x 2296-505X ; $v v. 355
505 0 $a 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.
520 $a 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.
650 0 $a Arakelov theory. $3 861059
650 1 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Number Theory. $3 274059
700 1 $a Moriwaki, Atsushi. $3 861058
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Progress in mathematics ; $v v.295. $3 558269
856 4 0 $u https://doi.org/10.1007/978-3-031-61668-6
950 $a Mathematics and Statistics (SpringerNature-11649)