$\ell$-adic étale cohomology of the moduli of stable elliptic fibrations

Abstract

We determine the $\ell$-adic étale cohomology and the eigenvalues of the geometric Frobenius for the moduli stack ${\mathcal{L}}_{1,12n}:={\mathrm{Hom}}_n({\mathbb{P}}^1,{\overline{\mathcal{M}}}_{1,1})$ of stable elliptic fibrations over ${\mathbb{P}}^1$ with $12n$ nodal singular fibers and a marked Weierstrass section over ${\overline{\mathbb{F}}}_q$ with $\mathrm{char}({\overline{\mathbb{F}}}_q)\ne 2,3$.

This paper is superseded by a newer paper, entitled "Étale cohomological stability of the moduli space of stable elliptic surfaces" arXiv:2207.02496 (by O. Banerjee, J. Park, and J. Schmitt)

References in corpus (3)

• The Grothendieck group of algebraic stacks
• The structure of the tautological ring in genus one
• L-series of Artin stacks over finite fields