DE RHAM–WITT COHOMOLOGY FOR A PROPER AND SMOOTH MORPHISM

By A. Langer, T. Zink. Journal of the Institute of Mathematics of Jussieu, 2004

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The basic geometry of Witt vectors, I: The affine case (2008, methodology): “ooth maps are false. In the context of p-typical Witt vectors, where we have momentarily put ourselves, this result has already been established by Illusie [22] for all Fp-algebras and by Langer–Zink [27] for Zp-algebras under certain ﬁniteness conditions, such as being of ﬁnite type. Their argument”
The basic geometry of Witt vectors. II: Spaces (2010, unknown): “In their appendix, Langer and Zink [35] constructed the p-typical Witt space of a general Zp-scheme X .”
The basic geometry of Witt vectors (2008, background): “Then W ∗1 (X) is the coequalizer in the category of algebraic spaces of the two maps X0 i1◦F // i2 // X ∐X, where ij : X0 → X ∐X denotes the canonical closed immersion into the j-th component of X ∐X and F is the absolute Frobenius endomorphism of X0.”
Integral p$p$-adic Hodge theory (2016, unknown): “Its proof relies on a relation to the de Rham–Witt complex of Langer–Zink [51].”