2017/06/16 by Annette Huber, Annette Huber-Klawitter, Shane Kelly
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Coherent sheaf #Differential (mechanical device) #Differential form #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Resolution (logic) #Sheaf #math.AG
paper · pdf · doi:10.2140/ant.2018.12.649
published as Alg. Number Th. 12 (2018) 649-692 · 37 pages
arxiv created 2017/06/16 · openalex created_date 2017/06/23 · openalex publication_date 2018/06/12 · arxiv updated 2018/06/20 · openalex updated_date 2026/08/05
This paper continues our study of the sheaf associated to Kähler differentials in the cdh-topology and its cousins, in positive characteristic, without assuming resolution of singularities. The picture for the sheaves themselves is now fairly complete. We give a calculation [math] in terms of the seminormalisation. We observe that the category of representable cdh-sheaves is equivalent to the category of seminormal varieties. We conclude by proposing some possible connections to Berkovich spaces and [math] -singularities in the last section. The tools developed for the case of differential forms also apply in other contexts and should be of independent interest.