Crystallinity for syntomic cohomology, étale cohomology, and algebraic $K$-theory

Jeremy Hahn, Ishan Levy, Andrew Senger

We prove for $n\ge c-1$ that the functor taking an animated ring $R$ to its mod $(p^c,v_1^{p^n})$ syntomic cohomology factors through the functor $R\mapsto R/p^{c(n+2)}$, a pheno…