Algebra/Toplogy seminar

Algebra/Toplogy seminar

Matthew Morrow, Continuous K-theory in characteristic p

The p-adic K-theory of a ring of characteristic p is reasonably well understood if the ring is smooth, thanks to results of Bloch--Kato--Gabber and Geisser--Levine relating K-theory, Milnor K-theory, de Rham--Witt groups, and motivic cohomology in such situations. I will explain how analogous results can be established for continuous K-theory of formal schemes in characteristic p, e.g., for the groups $K_n(\mathbb F_p[t_1,\dots,t_c]/(t_1,\dots,t_c)^s)/p^i$ as $s\to\infty$, and sketch some applications to the infinitesimal deformation theory of algebraic cycles.