The topological realization of a simplicial presheaf

Abstract

The purpose of this article is to define the topological realization of a simplicial presheaf and to prove (under appropriate conditions) that it is homotopy-invariant under Illusie weak equivalence. In particular this applies to the site of schemes over $Spec (\cc)$ with the etale or Zariski topologies. As an application we show how to calculate the topological realization of a Deligne-Mumford stack. At the end we speculate on how to extend this to the case of $n$-topoi.

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Cited by in corpus (4)

• Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
• A Giraud-type characterization of the simplicial categories associated to closed model categories as $\infty$-pretopoi
• The homology of moduli stacks of complexes
• Universal structures in $\mathbb{C}$-linear enumerative invariant theories