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With enough enthusiasm, I would try to learn about crystalline cohomology and the de-Rham-Witt complex from the homonymous article by Illusie:

Illusie, Luc. Complexe de deRham-Witt et cohomologie cristalline. (French) Ann. Sci. École Norm. Sup. (4) 12 (1979), no. 4, 501--661. MR0565469 (82d:14013)

Fortunately, it is publicly available at:

http://archive.numdam.org/ARCHIVE/ASENS/ASENS_1979_4_12_4/ASENS_1979_4_12_4_501_0/ASENS_1979_4_12_4_501_0.pdf