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The Arithmetic Hodge-Index Theorem and Rigidity of Algebraic Dynamical Systems over Function Fields
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | The Arithmetic Hodge-Index Theorem and Rigidity of Algebraic Dynamical Systems over Function Fields. |
| 개인저자 | Carney, Alexander. |
| 단체저자명 | University of California, Berkeley. Mathematics. |
| 발행사항 | [S.l.]: University of California, Berkeley., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 60 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04B. Dissertation Abstract International |
| ISBN | 9781085792615 |
| 학위논문주기 | Thesis (Ph.D.)--University of California, Berkeley, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Advisor: Yuan, Xinyi. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | 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. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
