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Algebraic cycles and crystalline cohomology. (arXiv:1504.08181v5 [math.AG] UPDATED)

来源于:arXiv
We show that additive higher Chow groups of S. Bloch and H. Esnault of smooth varieties over an arbitrary field induce a Zariski sheaf of pro-differential graded algebras, whose Milnor range is isomorphic to the Zariski sheaf of the big de Rham-Witt complexes of L. Hesselholt and I. Madsen. When the characteristic $p$ of the field is positive, the Zariski hypercohomology of the $p$-typical part of the sheaves arising from additive higher Chow groups computes the crystalline cohomology of smooth varieties. This revisits the 1970s results of S. Bloch and L. Illusie on crystalline cohomology, this time from algebraic cycles. 查看全文>>