标题： 关于在截断的Witt向量上的光滑概形的代数$K$-理论 显示英文标题

标题： On the algebraic $K$-theory of smooth schemes over truncated Witt vectors

摘要： 利用布伦定理，将相对代数$K$-理论与相对循环同调联系起来，我们计算了在$W_n(k)$上的$p$-adic光滑概形的某些相对代数$K$-群，其中$k$是特征为$p$的完美域。 受这一结果以及布洛克、埃斯纳尔特和克茨工作的启发，我们定义了无穷小动机复形，然后在一定范围内证明了一个带有整系数的相对陈类同构。 这在代数$K$-理论中的无穷小变形上产生了直接后果，这与$p$-adic变分Hodge猜想有关。 显示英文摘要

摘要： Using Brun's theorem relating the relative algebraic $K$-theory and the relative cyclic homology, we compute certain relative algebraic $K$-groups of a $p$-adic smooth scheme over $W_n(k)$, where $k$ is a perfect field of characteristic $p$. Inspired by this result and the work of Bloch, Esnault, and Kerz, we define the infinitesimal motivic complexes, and then show a relative Chern character isomorphism with integral coefficients in a range. This has a direct consequence on infinitesimal deformations in algebraic $K$-theory, which is related to the $p$-adic variational Hodge conjecture.