Moduli Spaces of Shtukas over the Projective Line

de Frutos-Fernández, María Inés

Journal de théorie des nombres de Bordeaux, Volume 34 (2022) no. 2, pp. 393-418.

We provide explicit equations for moduli spaces of Drinfeld shtukas over the projective line with $\Gamma \left(N\right)$, ${\Gamma }_1\left(N\right)$ and ${\Gamma }_0\left(N\right)$ level structures, where $N$ is an effective divisor on ${\mathbb{P}}^1$. If the degree of $N$ is high enough, these moduli spaces are relative surfaces. We study some invariants of the moduli space of shtukas with ${\Gamma }_0\left(N\right)$ level structure for several degree $4$ divisors on ${\mathbb{P}}^1$.

On donne des équations explicites pour des espaces de modules de chtoucas de Drinfeld sur la droite projective avec structures de niveau $\Gamma \left(N\right)$, ${\Gamma }_1\left(N\right)$ et ${\Gamma }_0\left(N\right)$, où $N$ désigne un diviseur effectif sur ${\mathbb{P}}^1$. Si le degré du diviseur $N$ est suffisamment grand, ces espaces de modules sont des surfaces relatives. On étudie certains invariants de l’espace de modules de chtoucas avec structures de niveau ${\Gamma }_0\left(N\right)$ pour plusieurs diviseurs de degré $4$ sur ${\mathbb{P}}^1$.

Classification: 11G09, 14H60, 11G18
Keywords: Drinfeld shtukas, moduli spaces, Kodaira types

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