Abstract: Let X be a smooth proper scheme over a p-adic field such that X has a good reduction. Inspired by the de Rham comparison theorem in complex geometry, Grothendieck asked if there is a "mysterious functor" relating etale cohomology of the generic fiber and crystalline cohomology of the special fiber. This question was answered by work of many people, including Fontaine and Faltings. In particular, this motivates the definition of a p-adic Galois representation being crystalline, generalizing the etale cohomology of X as above. In this talk, we will give an overview for the prismatic approach of Bhatt-Scholze on crystalline representations. Moreover, jointly with Emanuel Reinecke, we will consider the higher dimensional generalization of this approach on crystalline local systems.
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Link: https://zoom.us/j/81805953631?pwd=VXFLaUpFZm1kZ285bklKWkQ4OE01Zz09
ID: 818 0595 3631
Password: 746304
