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math.NT2008★ 9 cited
The Geometric Bogomolov Conjecture for Small Genus Curves
X. W. C. Faber
The Bogomolov Conjecture is a finiteness statement about algebraic points of small height on a smooth complete curve defined over a global field. We verify an effective form of the…
math.NT2005
On the Finite Field Kakeya Problem in Two Dimensions
X. W. C. Faber
A two-dimensional Besicovitch set over a finite field is a subset of the finite plane containing a line in each direction. In this paper, we conjecture a sharp lower bound for the…