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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>>