Local and canonical heights of subvarieties

By Walter Gubler. 2003

54 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c9b8c66e83c7a06561dd353ad2ff59a812d92958

Citations in the corpus

• Equidistribution over function fields (2008, methodology): “height is given as a sum of local heights λ(Z, v) with respect to suitable meromorphic sections s0, . . . , st (see [ Gu2 ], §11).”
• Tropical varieties for non-archimedean analytic spaces (2006, methodology): “ a larger class g+ X with the same properties. Since canonical metrics of odd line bundles are cohomologically semipositive, the new class ˆgX includes all canonical metrics on abelian varieties (see [Gu3], §10). All results of this section hold for this ˆgX as well. Let Xbe a smooth complete variet”
• Equidistribution in Families of Abelian Varieties and Uniformity (2021, unknown): “We then define (1) b As [ n ] preserves the fibers of π , the limit superior in (1) specializes to an ordinary N´eron-Tate height if X is completely contained in such a fiber ([38, Theorem 11.18]).”
• The Bogomolov conjecture for totally degenerate abelian varieties (2006, methodology): “ (e) If k k0,v,...,k kd,v are all ˆg + X,v-metrics, then the local height is non-negative. (f) If k k0,v,...,k kd,v are formal metrics, then the local height is given by 2.5. For a proof, we refer to [Gu2], Theorem 10.6. 2.7 A continuous function g on Xan v induces a metric k kg,v on OX determined b”