Bhatt--Morrow--Scholze constructed a motivic filtration on the topological cyclic homology of an animated ring whose associated graded quotients (called syntomic complexes) are a sort of Frobenius fixed points of prismatic cohomology. I will describe an identification of the syntomic complexes in the case of a regular ring, with the p-adic \'etale Tate twists of Geisser--Sato--Schneider. The key ingredient is a mixed characteristic analog of the Cartier isomorphism (essentially, the Segal conjecture in THH). This is joint work with Bhargav Bhatt.