Rigid Cohomology and de Rham-Witt Complexes
Pierre Berthelot
Université de Rennes I, France
![Rigid Cohomology and de Rham-Witt Complexes cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rsmup-volume-128.png&w=3840&q=90)
Abstract
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. 287–344
DOI 10.4171/RSMUP/128-8