摘要：In this talk, I will give a brief construction of the crystalline comparison isomorphisms for proper smooth formal schemes, and explain certain key techiniques.Such isomorphisms hold for coefficients and in the relative setting, i.e. for p-adic etale cohomology with coefficients in Z_p-local systems, and for proper smooth morphisms of smooth formal schemes.The proof is formulated in terms of the pro-etale site defined by Scholze.Another ingredient for the proof is the Poincare lemma for crystalline period sheaves, for which we adapt the idea of Andreatta and Iovita.This is part of a joint project with Jilong Tong.

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