Cohomological descent of rigid cohomology for proper coverings
This paper is Tsuzuki's ingenious proof of descent for proper coverings of the rigid cohomology of Berthelot. In classical (complex) Hodge theory, cohomological descent of singular cohomology is combined with resolution of singularities to give meaning to mixed Hodge structure on the singular cohomology of a possible singular variety. Similarly, the result of Tsuzuki can be used in combination with \textit{A. J. de Jong}'s alterations [Publ. Math., Inst. Hautes Étud. Sci. 83, 51--93 (1996; Zbl 0916.14005)] to prove that rigid cohomology of a separated scheme of finite type over a field of positive characteristic has bijective Frobenius and is finite dimensional (this was also proven by \textit{E. Grosse-Klönne} [Duke Math. J. 113, No. 1, 57--91 (2002; Zbl 1057.14023)] by a different method). That is just one of the applications.
scientific article; zbMATH DE number 1965459