Algebra/Topology seminar

Speaker: Ishan Levy

Title: Crystallinity for reduced syntomic cohomology and K(Z/p^n)/(p,v_1)

Abstract: I will explain joint work with Jeremy Hahn and Andrew Senger, where we prove crystallinity properties for p-adic cohomology theories such as prismatic and syntomic cohomology. In particular, we prove that syntomic cohomology mod (p,v_1^{p^{n-2}}) only depends on R/p^n. Applying this to the case of R = Z/p^n, and using the motivic filtration of Bhatt—Morrow—Scholze, we can in particular completely compute \pi_*K(Z/p^n)/(p,v_1^{p^{n-2}-1}) for p odd, which is the first complete computation towards the homotopy groups of K(Z/p^n).