Abstract
Abstract
We construct Galois covers
{X^{r,k}(N)}
over
{{\mathbb{P}}^{1}/{\mathbb{F}}_{q}(T)}
with Galois groups close to
{{\rm GL}(r,{\mathbb{F}}_{q}[T]/(N))}
(
{r\geq 3}
) and rationality and ramification properties similar to those of
classical modular curves
{X(N)}
over
{{\mathbb{P}}^{1}/{\mathbb{Q}}}
. As application we find plenty of good
towers (with
\limsup{\frac{\text{number~{}of~{}rational~{}points}}{{\rm genus}}>0}
) of curves over
the field
{{\mathbb{F}}_{q^{r}}}
with
{q^{r}}
elements.
Subject
Applied Mathematics,General Mathematics
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