• Corpus ID: 119249617

On $q$-de Rham cohomology via $\Lambda$-rings

  title={On \$q\$-de Rham cohomology via \$\Lambda\$-rings},
We show that Aomoto’s q-deformation of de Rham cohomology arises as a natural cohomology theory for Λ-rings. Moreover, Scholze’s (q− 1)-adic completion of q-de Rham cohomology depends only on the Adams operations at each residue characteristic. This gives a fully functorial cohomology theory, including a lift of the Cartier isomorphism, for smooth formal schemes in mixed characteristic equipped with a suitable lift of Frobenius. If we attach p-power roots of q, the resulting theory is… 


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