| Résume | In this talk, we will explain that for any proper smooth (formal) scheme over \(\mathcal{O}_K\) , where \(\mathcal{O}_K\) is the ring of integers in a complete discretely valued nonarchimedean extension K of \(\mathbb{Q}_p\) with perfect residue field k and ramification degree e, the i-th Breuil-Kisin cohomology group and its Hodge-Tate specialization admit nice decompositions when ie < p−1. We will see this can be used to prove the integral comparison theorems about p-adic etale cohomology and crystalline cohomology, which were proven before by Fontaine-Messing and Caruso. |
