Arithmetic of the Moduli of Fibrations

Zoom ID: 919 6497 4060.
For password please contact Pieter Moree (moree@mpim...).

We will first consider the explicit formulation of the moduli
stacks of fibered algebraic surfaces as the moduli stacks of rational
curves on $\overline{\mathcal{M}}_{g,n}$.

This will lead us to exact arithmetic invariants on those moduli stacks
via motives in the Grothendieck ring of stacks introduced by the late
Torsten Ekedahl that will, in turn, render their point counts over
finite fields. We then enumerate elliptic & hyperelliptic curves over
$\mathbb{P}_{\mathbb{F}_q}^{1}$ with precise lower order terms ordered
by bounded discriminant height.

Along the way, we will glance at 2 important analogies in number theory
& geometry that are

1. Global fields analogy,
2. Rational points & Rational curves.