2015/09/07 by Alexis Bouthier, Bouthier, Alexis
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1509.02203
openalex publication_date 2015/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a structure theorem on the arc space of a k-scheme of finite type. More precisely, we show that the arc space is locally for the pro-smooth toplogy a product of an infinite dimensional affine space and of a non-noetherian scheme, stratified by k-schemes of finite type, that glues the different formal completions of the arc space. This statement globalizes Drinfeld-Grinberg-Kazhdan's theorem and proves a conjecture of Kollar and Nemethi. Then, we use this theorem to construct a derived category of constructible sheaves, stable by six operations and we show a finiteness result for the cohomology.