北京雁栖湖应用数学研究院

Prismatic cohomology, which is developed in a recent work of Bhatt-Scholze, is a cohomology theory for schemes over p-adic rings. It is considered to be an overarching cohomology theory in p-adic geometry, unifying etale, de Rham, and crystalline cohomology. Due to wide-ranging applications in p-adic Hodge theory and p-adic Galois representations, it is one of the central topics of active research. In this course, we will start by going over motivational background in p-adic cohomology theories, and then give a rough overview of main ideas and results in the paper "Prisms and prismatic cohomology" by Bhatt-Scholze. If time permits, we will also briefly discuss how the prismatic theory may reveal a deeper understanding of p-adic Galois representations.