The Bogomolov conjecture for totally degenerate abelian varieties
نویسنده
چکیده
Let K = k(B) be a function field of an integral projective variety B over the algebraically closed field k such that B is regular in codimension 1. The set of places MB is given by the prime divisors of B. We fix an ample class c on B. If we count every prime divisor Y with weight deg c (Y ), then the valuations ordY lead to a product formula on K and hence to a theory of heights (see [La] or [BG], Section 1.5). The algebraic closure of K is denoted by K. For an abelian variety A over K which is totally degenerate at some place v ∈ MB (see §5 for definition), we will prove the Bogomolov conjecture:
منابع مشابه
A Generalization of Conjectures of Bogomolov and Lang
[1] G. Faltings, Diophantine approximation on abelian varieties, Ann. of Math., 133 (1991), 549-576. [2] M. Hindry, Autour d'une conjecture de Serge Lang, Invent. math., 94 (1988), 575-603. [3] B. Poonen, Mordell-Lang plus Bogomolov, Invent. math., 137 (1999), 413-425. [4] M. McQuillan, Divison points on semi-abelian varieties, Invent. math., 120 (1995), 143-159. [5] A. Moriwaki, Arithmetic hei...
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تاریخ انتشار 2006