A sharp Bogomolov-type bound
  We prove a sharp lower bound for the essential minimum of a non-translate variety in certain abelian varieties. This uses and generalises a result of Galateau. Our bound is a new step in direction of an abelian analogue by David and Philippon of a toric conjecture of Amoroso and David and has applications in the framework of anomalous intersections. 
Sara Checcoli, Francesco Veneziano, Evelina Viada
math.NT