23 citations · 149 across the 28 of their papers we have counts for
34 papers
Compressive Domains and a Bound for the Number of Components of the Fixed Locus of a Self-Map of the Berkovich Line
Xander Faber, Niladri Patra
We introduce the notion of a "compressive domain" for the action of a rational function on the Berkovich projective line over a complete nontrivially-valued algebraically closed no…
Structure of the Components of the Fixed Locus of a Self-Map of the Berkovich Line
Xander Faber, Niladri Patra
We describe the local and global structure of the fixed locus for the action of a rational function on the Berkovich projective line over a complete nontrivially-valued algebraical…
Ramified Approximation and Semistable Reduction
Xander Faber
Let be a complete discretely valued field. An extension is "weakly totally ramified" if the residue extension is purely inseparable. We sharpen a result of Ax by showing…
On the Maximum Gonality of a Curve over a Finite Field
Xander Faber, Jon Grantham, Everett W. Howe
The gonality of a smooth geometrically connected curve over a field is the smallest degree of a nonconstant -morphism from the curve to the projective line. In general, the…
New families satisfying the Dynamical Uniform Boundedness Principle over function fields
John R. Doyle, Xander Faber
We extend a technique, originally due to the first author and Poonen, for proving cases of the Strong Uniform Boundedness Principle (SUBP) in algebraic dynamics over function field…
On abelian covers of the projective line with fixed gonality and many rational points
Xander Faber, Floris Vermeulen
A smooth geometrically connected curve over the finite field with gonality has at most rational points. The first author and Grantham conjectured that…