Speaker: Xiaowen Hu ( Great Bay University)
Time: 2025-11-21 10:30-11:30
Location: 910, SIMIS
摘要：
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.
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