Let be a perfect field of characteristic . For separated -schemes of finite type, we explain how rigid cohomology with compact supports can be computed as the cohomology of certain de Rham-Witt complexes with coefficients. This result generalizes the classical comparison theorem of Bloch-Illusie for proper and smooth schemes. In the proof, the key step is an extension of the Bloch-Illusie theorem to the case of cohomologies relative to with coefficients in a crystal that is only assumed to be flat over .
Cite this article
Pierre Berthelot, Rigid Cohomology and de Rham-Witt Complexes. Rend. Sem. Mat. Univ. Padova 128 (2012), pp. 287–344DOI 10.4171/RSMUP/128-8