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math.NT2006★ 68 cited
The Bogomolov conjecture for totally degenerate abelian varieties
Walter Gubler
We prove the Bogomolov conjecture for an abelian variety A over a function field which is totally degenerate at a place v. We adapt Zhang's proof of the number field case replacing…
math.NT2006★ 59 cited
Tropical varieties for non-archimedean analytic spaces
Walter Gubler
We associate to an analytic subvariety of a torus a tropical variety. In the first part, we generalize the results from tropical algebraic geometry to this non-archimedean analytic…