Rendiconti del Seminario Matematico della Università di Padova

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Volume 128, 2012, pp. 287–344
DOI: 10.4171/RSMUP/128-8

Rigid Cohomology and de Rham-Witt Complexes

Pierre Berthelot[1]

(1) IRMAR, Université de Rennes I, Campus de Beaulieu, 35042, Rennes CEDEX, France

Let $k$ be a perfect field of characteristic $p > 0, W_n =ˆ W_n(k)$. For separated $k$-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 $W_n$ with coefficients in a crystal that is only assumed to be flat over $W_n$.

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Berthelot Pierre: Rigid Cohomology and de Rham-Witt Complexes. Rend. Sem. Mat. Univ. Padova 128 (2012), 287-344. doi: 10.4171/RSMUP/128-8