LDR | | 00000nam u2200205 4500 |
001 | | 000000434450 |
005 | | 20200226151051 |
008 | | 200131s2019 ||||||||||||||||| ||eng d |
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▼a 9781085792615 |
035 | |
▼a (MiAaPQ)AAI13885593 |
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▼a MiAaPQ
▼c MiAaPQ
▼d 247004 |
082 | 0 |
▼a 510 |
100 | 1 |
▼a Carney, Alexander. |
245 | 14 |
▼a The Arithmetic Hodge-Index Theorem and Rigidity of Algebraic Dynamical Systems over Function Fields. |
260 | |
▼a [S.l.]:
▼b University of California, Berkeley.,
▼c 2019. |
260 | 1 |
▼a Ann Arbor:
▼b ProQuest Dissertations & Theses,
▼c 2019. |
300 | |
▼a 60 p. |
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▼a Source: Dissertations Abstracts International, Volume: 81-04, Section: B. |
500 | |
▼a Advisor: Yuan, Xinyi. |
502 | 1 |
▼a Thesis (Ph.D.)--University of California, Berkeley, 2019. |
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▼a This item must not be sold to any third party vendors. |
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▼a In one of the fundamental results of Arakelov's arithmetic intersection theory, Faltings and Hriljac (independently) proved the Hodge-index theorem for arithmetic surfaces by relating the intersection pairing to the negative of the Neron-Tate height pairing. More recently, Moriwaki and Yuan-Zhang generalized this to higher dimension. In this work, we extend these results to projective varieties over transcendence degree one function fields. The new challenge is dealing with non-constant but numerically trivial line bundles coming from the constant field via Chow's K/k-image functor.As an application of the Hodge-index theorem to heights defined by intersections of adelic metrized line bundles, we also prove a rigidity theorem for the set height zero points of polarized algebraic dynamical systems over function fields. In the special case of a global field, this gives a rigidity theorem for preperiodic points, generalizing previous work of Mimar, Baker-DeMarco, and Yuan-Zhang. |
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▼a School code: 0028. |
650 | 4 |
▼a Mathematics. |
690 | |
▼a 0405 |
710 | 20 |
▼a University of California, Berkeley.
▼b Mathematics. |
773 | 0 |
▼t Dissertations Abstracts International
▼g 81-04B. |
773 | |
▼t Dissertation Abstract International |
790 | |
▼a 0028 |
791 | |
▼a Ph.D. |
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▼a 2019 |
793 | |
▼a English |
856 | 40 |
▼u http://www.riss.kr/pdu/ddodLink.do?id=T15491453
▼n KERIS
▼z 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
980 | |
▼a 202002
▼f 2020 |
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▼a ***1816162 |
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▼a E-BOOK |