Abstract

Kisin module is a powerful tool in p-adic Hodge theory to understand reduction of crystalline representation. Prismatic cohomology can be thought as a geometric realization of Kisin module, which is expected to provide better understanding for etale cohomology and other related cohomologies. In this talk, we exhibit a concrete example of such expectation: We use prismatic cohomlogy and (derived) de Rham cohomology  to improve a classical result of Breuil and Caruso on comparison between torsion crystalline cohomology and torsion etale cohomology. This is joint work with Shizhang Li.