Arithmetic height functions over finitely generated fields
نویسندگان
چکیده
منابع مشابه
Arithmetic Height Functions over Finitely Generated Fields
In this paper, we propose a new height function for a variety defined over a finitely generated field overQ. For this height function, we will prove Northcott’s theorem and Bogomolov’s conjecture, so that we can recover the original Raynaud’s theorem (Manin-Mumford’s conjecture). CONTENTS Introduction 1 1. Arakelov intersection theory 3 2. Arithmetically positive hermitian line bundles 6 3. Ari...
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This paper is the sequel of [2]. In [4], S. Zhang defined the canonical height of subvarieties of an abelian variety over a number field in terms of adelic metrics. In this paper, we generalize it to an abelian variety defined over a finitely generated field over Q. Our way is slightly different from his method. Instead of using adelic metrics directly, we introduce an adelic sequence and an ad...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2000
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s002220050358