Rigid Cohomology and de Rham-Witt Complexes

  • Pierre Berthelot

    Université de Rennes I, France


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

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