On $q$-de Rham cohomology via $Λ$-rings

J. P. Pridham

Published 2016-08-25Version 1

In this note, we show that Aomoto's $q$-deformation of de Rham cohomology is a natural cohomology theory for $\Lambda$-rings. Moreover, the $(q-1)$-adically completed theory depends only on the Adams operations at each residue characteristic. In particular, this gives a fully functorial cohomology theory for schemes in mixed characteristic equipped with a lift of Frobenius.