Log Manin's conjecture for the Heisenberg group

Material type: 博士論文

Author: 肖, 歓ほか

Publisher: 熊本大学

Publication date: 2022-09-26

Material Format: Digital

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Name of awarding university/degree: 熊本大学,博士（理学）

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Note (General)：: We study the distribution of Campana points of bounded height on biequivariant compactifications of the Heisenberg group, and prove the log Manin conj...

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Material Type: 博士論文
Title: Log Manin's conjecture for the Heisenberg group
Author/Editor: 肖, 歓
Huan, XIAO
Author Heading: 肖, 歓
Huan, XIAO
Publication, Distribution, etc.: 熊本大学
Publication Date: 2022-09-26
Publication Date (W3CDTF): 2022-09-26
Alternative Title: ハイゼンベルク群に対するログマニン予想
Degree grantor/type: 熊本大学
Date Granted: 2022-09-26
Dissertation Number: 甲理学第249号
Degree Type: 博士（理学）
Text Language Code: eng
Subject Heading: 377.5
Target Audience: 一般
Note (General): We study the distribution of Campana points of bounded height on biequivariant compactifications of the Heisenberg group, and prove the log Manin conjecture introduced by M. Pieropan, A. Smeets, S. Tanimoto and A. Varilly-Alvarado, on the asymptotic formula for the number of such Campana points.In Chapter 1 we review the notions of adelically metrized line bundles and heights on adelic spaces. They are basic for the height functions and height zeta functions associated to a given line bundle.In Chapter 2 we review the classical Manin's conjecture including its background, formulation, and various approaches and progress toward it.In Chapter 3 we recall the log Manin conjecture introduced by M. Pieropan, A. Smeets, S. Tanimoto and A. Varilly-Alvarado. The log Manin conjecture concerns the distribution of Campana points of bounded height on Fano Campana orbifolds over number fields. We review the background, the statement and the progress toward the log Manin conjecture.In Chapter 4 we review the theory of the Heisenberg group, especially its representation theory. We discuss the height zeta function associated with Campana points on biequivariant compactifications of the Heisenberg group.In Chapter 5 we prove the log Manin conjecture by the height zeta function method, for biequivaraint compactifications of the Heisenberg group over the field of rational numbers under mild conditions.
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