学术报告（胡晓文 2025.10.23）

摘要： Around 2013, Bloch, Kerz, and Esnault proposed a K-theoretic approach to the $p$-adic variational Hodge conjecture, and showed a formal version of this conjecture. In this talk, I will recall the background of this conjecture and give an introduction to the related notions, e.g., algebraic K-theory, cyclic homology,  motivic complexes, etc.  Then I will sketch my recent progress on the infinitesimal version. Especially, we will see that computation of certain relative cyclic homology leads to a natural definition of infinitesimal motivic complexes, and that we can show a Chern character isomorphism using mod p products and certain functorial properties.