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The de Rham–Witt complex is invariant under semi-normalization (and
recovers the semi-normalization of a ring).
Cover §§6.1-6.2 and §§6.5-6.6, with a focus on Proposition 6.2.1, Corol?lary 6.5.2, and Theorem 6.5.3. As time permits, introduce crystalline
cohomology (as the cohomology of the structure sheaf on the crystalline
site relative to the divided power ring (Zp,(p)), see for example the book
by Berthelot or Tag 07GI in the Stacks project) and cover §6.4.