Prismatic cohomology and p-adic homotopy theory.

Historically, it was known by the work of Artin and Mazur that the ℓ -adic homotopy type of a smooth complex variety with good reduction mod p can be recovered from the reduction mod p, where ℓ is not p. This short note removes this last constraint, with an observation about the recent theory of prismatic cohomology developed by Bhatt and Scholze. In particular, by applying a functor of Mandell, we see that the étale comparison theorem in the prismatic theory reproduces the p-adic homotopy type for a smooth complex variety with good reduction mod p. [ABSTRACT FROM AUTHOR]