Illusie, Luc A new approach to de Rham-Witt complexes, after Bhatt, Lurie, and Mathew. (English) Zbl 1490.14031 Rend. Semin. Mat. Univ. Padova 146, 177-221 (2021). This paper is a report on [B. Bhatt et al., Revisiting the de Rham-Witt complex. Paris: Société Mathématique de France (SMF) (2021; Zbl 1478.14038)]. As the author said:“My aim ... is 4-fold:– put [loc. cit.] in a broader historical perspective;– give a short and (as much as possible) self-contained summary of its basic definitions, constructions, and properties;– discuss examples;– discuss open questions and perspectives.”Since this report was written before the final publication of [loc. cit.], a few proofs presented here are different from the published version of [loc. cit.]. These old proofs are sometimes more direct, if slightly less conceptual, than those appeared in the published version. Reviewer: Dingxin Zhang (Beijing) Cited in 1 Document MSC: 14F30 \(p\)-adic cohomology, crystalline cohomology 14F40 de Rham cohomology and algebraic geometry 14G17 Positive characteristic ground fields in algebraic geometry 14B05 Singularities in algebraic geometry Keywords:Cartier isomorphism; crystalline cohomology; de Rham complex; de Rham cohomology; de Rham-Witt complex; Dieudonné complex; Frobenius morphism; Kodaira vanishing; lifting; Nygaard filtration; \(p\)-adic Hodge theory; rigid cohomology; seminormal ring; slope spectral sequence; toric singularity; Witt vectors Citations:Zbl 1478.14038 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] P. B , Cohomologie cristalline des schémas de caractéristique p > 0, Lec-ture Notes in Mathematics, 407, Springer, Berlin etc., 1974. · Zbl 0298.14012 [2] P. B -S. B -H. E , On Witt vector cohomology for singular varieties, Compos. Math. 143 (2007), no. 2, pp. 363-392. · Zbl 1213.14040 [3] P. B -A. 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