Stacky approach and p-adic coefficients

A stacky approach to a cohomology theory is often useful for distilling its core properties, for instance in establishing a six-functor formalism and studying its coefficients. In this talk, using the theory of Gelfand stacks, we will study stacky approaches to the theory of p-adic coefficients, including rigid cohomology, overconvergent isocrystals, and arithmetic D-modules, and present some applications.