Niklas Kipp: A solid Syntomification

We will learn a strategy to obtain a well behaved six-functor formalism for Syntomic cohomology of p-adic formal schemes as defined by Bhatt-Morrow-Scholze. Here well behaved mainly refers to this six-functor formalism generalising Poincaré duality (which was proven by Longke Tang in the smooth and proper case) to smooth morphisms using a version of compactly supported syntomic cohomology. Concretely, we will recall some aspects of the stacky approach to Prismatic/Syntomic cohomology (following Bhatt-Lurie and Drinfeld) as well as some aspects of the theory of (Solid) analytic stacks (following Clausen-Scholze).