Number Theory Seminar
Chirag Singhal
University of Illinois at Chicago
The field of definition of a Drinfeld module (II)
Abstract: Let $A = \mathbb{F}_q[T]$ be the ring of polynomials in the indeterminate $T$ and
with coefficients in the finite field $\mathbb{F}_q$ with $q$ elements,
and let $K$ be an $A$-field.
Let $\phi$ be a Drinfeld $A$-module over $K$, of rank $r \geq 2$.
Denote by $j_{k_1, \ldots, k_{l}}^{s_1, \ldots, s_{l}}(\phi)$
the family of $j$-invariants associated to $\phi$ by I.Y. Potemine.
Motivated by an argument of G. Shimura used in the context of abelian varieties,
we show that
$\mathbb{F}_q(T, j_{k_1, \ldots, k_{l}}^{s_1, \ldots, s_{l}}(\phi))$
is a field of definition for $\phi$.
Friday March 17, 2023 at 12:00 PM in 612 SEO