The Bogomolov conjecture for totally degenerate abelian varieties
By Walter Gubler. 2006
89 citations recorded by the source corpus.
We prove the Bogomolov conjecture for a totally degenerate abelian variety A over a function field. We adapt Zhang’s proof of the number field case replacing the complex analytic tools by tropical analytic geometry. A key step is the tropical equidistribution theorem for A at the totally degenerate place v. As a corollary, we obtain finiteness of torsion points with coordinates in the maximal unramified algebraic extension over v.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e7c957e213f609b9fbb34b29121df0cb73e3eaa4
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In Computational Theory and Mathematics
- Joseph Rabinoff
- Shou-wu Zhang
- Zubeyir Cinkir
- Walter Gubler
- Sam Payne
- Matthew Baker
- Martin Ulirsch
- David Jensen
In Geometry and Topology
- Zubeyir Cinkir
- Joseph Rabinoff
- Shou-wu Zhang
- Walter Gubler
- Xinyi Yuan
- Matthew Baker
- Sam Payne
- Martin Ulirsch
Citations in the corpus
- Tropical analytic geometry, Newton polygons, and tropical intersections (2010, methodology): “ubler [Gub07b] has used the combinatorial tructure on the tropicalization of a closed subspace of a polytopal subdomain in order to prove special cases of the Bogomolov conjecture over function fields [Gub07a]. The author has studied the tropicalization of the logarithm of a p-divisible formal group ”
- Equidistribution over function fields (2008, background): “This is proved in [ 13 ], 3.5, for ample symmetric line bundles.”
- Zhang’s Conjecture and the Effective Bogomolov Conjecture over function fields (2009, background): “Gubler [G] showed that the Bogomolov Conjecture is true for C if the Jacobian variety of C has”
- Gross–Schoen cycles and dualising sheaves (2008, result): “Some partial results have been obtained by Moriwaki [29], Yamaki [38], and Gubler [26].”