Differential forms in positive characteristic II: cdh-descent via functorial Riemann-Zariski spaces
- Resource Type
- Working Paper
- Authors
- Huber, Annette; Kelly, Shane
- Source
- Alg. Number Th. 12 (2018) 649-692
- Subject
- Mathematics - Algebraic Geometry
- Language
This paper continues our study of the sheaf associated to K\"ahler 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 $\mathcal{O}_{cdh}(X) \cong \mathcal{O}(X^{sn})$ 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 $F$-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.
Comment: 37 pages