1 citations · 4 across the 11 of their papers we have counts for
11 papers
Rational points on curves over function fields
Amilcar Pacheco, Fabien Pazuki
We provide in this paper an upper bound for the number of rational points on a curve defined over a one variable function field over a finite field. The bound only depends on the c…
Normal subgroups of fundamental groups of affine curves in positive characteristic II
Amilcar Pacheco, Pavel Zalesskii, Katherine F. Stevenson
Let be an algebraically closed field of characteristic and let be a smooth connected affine curve. Denote by its algebraic fundamental group. The goal of t…
Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic
Amilcar Pacheco, Pavel Zalesski, Katherine F. Stevenson
Let be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic of countable cardinality. Let…
Selmer groups of abelian varieties in extensions of function fields
Amilcar Pacheco
Let be a field of characteristic , $\cac$ a smooth geometrically connected curve defined over with function field $K:=k(\cac)$. Let be a non constant abelian varie…
On the rank of abelian varieties over function fields
Amilcar Pacheco
Let $\cac$ be a smooth projective curve defined over a number field , $A/k(\cac)$ an abelian variety and the $k(\cac)/k$-trace of . We estimate how the rank of $A(k(\…
On the variation of the rank of Jacobian varieties on unramified abelian towers over number fields
Amilcar Pacheco
Let be a smooth projective curve defined over a number field , a smooth projective curve of positive genus, the Jacobian variety of and the $k(C)/…