Speaker:  Andrew Senger (Harvard University)

Title:  On the K-theory of Z/pⁿ

Abstract:   

In this talk, I will explain how to compute the mod (p, v₁^pn) algebraic K theory of Z/pⁿ⁺² for n ≥ 0.  A key role is played by a new crystallinity result for syntomic cohomology: the mod (p, v₁^pn) syntomic cohomology of R only depends on R/p^n+2.  Our proof depends crucially on Drinfeld and Bhatt-Lurie’s stacky approach to syntomic cohomology.

This is joint work with Jeremy Hahn and Ishan Levy.