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European Mathematical Society Publishing House
2016-09-19 17:05:49
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
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128
2012
0
Rigid Cohomology and de Rham-Witt Complexes
Pierre
Berthelot
Université de Rennes I, RENNES CEDEX, FRANCE
Let $k$ be a perfect field of characteristic $p > 0, W_n = W_n(k)$. 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 $W_n$.
General
287
344
10.4171/RSMUP/128-8
http://www.ems-ph.org/doi/10.4171/RSMUP/128-8