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arXiv · 1207.6193

Completions and derived de Rham cohomology

Bhargav Bhatt
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Abstract

We show that Illusie's derived de Rham cohomology (Hodge-completed) coincides with Hartshorne's algebraic de Rham cohomology for a finite type map of noetherian schemes in characteristic 0; the case of lci morphisms was a result of Illusie. In particular, the E_1-differentials in the derived Hodge-to-de Rham spectral sequence for singular varieties are often non-zero. Another consequence is a completely elementary description of Hartshorne's algebraic de Rham cohomology: it is computed by the completed Amitsur complex for any variety in characteristic 0.

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Bhargav Bhatt. 2012-07-26. Completions and derived de Rham cohomology. https://arxiv.org/abs/1207.6193

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