走向现代数学学术报告 - 胡晓文副教授（No. 890)

报告题目：On the algebraic K-theory over truncated Witt vectors

报告时间：2025年12月10日 16:30

报告地点：东海岸校区-D实209

报 告 人：胡晓文 副教授（大湾区大学）

邀 请 人：陈哲 副教授

报告摘要：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 in low degrees compared to the $p$. Our results recover the above-mentioned of Bloch, Esnault, and Kerz, and lead to a reasonable definition of infinitesimal motivic complexes, and imply an infinitesimal version of the pVHC.

报告人简介：胡晓文，大湾区大学副教授。博士毕业于清华大学，主要研究镜像对称里的计数几何问题，包括Gromov-Witten不变量、希尔伯特概型等，近期研究兴趣为代数K理论。相关成果发表在 Adv Math、IMRN、Math Ann、Sci China Math 等期刊。