| LDR | | 00000nam u2200205 4500 |
| 001 | | 000000434450 |
| 005 | | 20200226151051 |
| 008 | | 200131s2019 ||||||||||||||||| ||eng d |
| 020 | |
▼a 9781085792615 |
| 035 | |
▼a (MiAaPQ)AAI13885593 |
| 040 | |
▼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. |
| 500 | |
▼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. |
| 506 | |
▼a This item must not be sold to any third party vendors. |
| 520 | |
▼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. |
| 590 | |
▼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. |
| 792 | |
▼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 |
| 990 | |
▼a ***1816162 |
| 991 | |
▼a E-BOOK |