Lower bounds for the height in one dimension

F. Amoroso and R. Dvornicich, "A Lower Bound for the Height in Abelian Extensions",  J. Number Theory 80 (2000),  no. 2, 260-272.

F. Amoroso and U. Zannier, "A relative Dobrowolski lower bound on abelian extensions", Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 29 (2000), no. 3, 711-727.

F. Amoroso and F. Delsinne, "Une minoration relative explicite pour la hauteur dans une extension d'une extension abélienne", Diophantine geometry, 1–24,
CRM Series, 4, Ed. Norm., Pisa, 2007.

F. Amoroso and U. Zannier, "A uniform relative Dobrowolski’s lower bound over abelian extensions", Bull. Lond. Math. Soc. 42 (2010), no. 3, 489–498.

F. Amoroso, S. David and U. Zannier, "On fields with the property (B)".  Proc. Amer. Math. Soc. To appear

Slides of my lectures at the winter school "Heights and Algebraic Numbers",  Tubingen, March 2-4, 2011