Abstract
Let O_K be a complete discrete valuation ring with perfect residue field, then Bhatt-Scholze recently proved that the category of lattices of crystalline representations of G_K is equivalent to the category of prismatic F-crystals on the absolute prismatic site over O_K. I will discuss two possible generalizations of their result. This talk is based on a joint work with Tong Liu and a joint work in progress with Tong Liu, Yong Suk Moon and Koji Shimizu.
