All Questions

For smooth proper schemes over $\mathbb{C}_p$, there is no canonical Hodge--Tate decomposition (but there is something close). Is there an analogue of this on the archimedean side? I thought about ...

Prismatic cohomology is a new theory developed by Bhatt and Scholze; see, for instance, these course notes. For the sake of the community, it would be great if the following question is discussed in ...

The proof of the Lefschetz Hyperplane theorem over $\mathbb{C}$ is well-known, and relies on Hodge theory in an important way. Does there exist an analogue of this theorem in positive characteristic, ...