Time：14:00-16:00, Wednesday, November 19 2025
Venue：E4-233
Speaker: Xiaowen Hu, Great Bay University
Title：On the algebraic K-theory over truncated Witt vectors
Abstract: Around 2013, Bloch, Esnault, and Kerz proposed a K-theoretic approach to the $p$-adic variational Hodge conjecture (pVHC), and showed a formal version of this conjecture. A crucial ingredient in their proof is the computation of the relative continuous K-theory of a smooth scheme over the ring of Witt vectors of a perfect field of characteristic $p$. The continuous K-theory is defined as the limit of the relative K-theory over the truncated Witt vectors. It is therefore desirable to know this relative K-theory exactly over the truncated Witt vectors of every length. In this talk, I will recall the background of pVHC and sketch a computation of this relative K-theory. Our results recover that of B-E-K and lead to a reasonable definition of infinitesimal motivic complexes and imply an infinitesimal version of pVHC.
