Tuesday 4 November 2025, 16:00 - 17:00 in HG00.071
Tommy Lundemo (Utrecht)
On the p-adic deformation problem: The case of semistable reduction
I will explain how the Hodge conjecture motivates the following problem in p-adic geometry: Given a smooth and proper variety over a discrete valuation ring, when does an element in the K-theory of its special fiber lift to one in the K-theory of the original variety? Strikingly, the corresponding “deformational” version of this problem is governed by the Hodge filtration on the de Rham cohomology of the generic fiber, as shown by work of Bloch--Esnault--Kerz and Antieau--Mathew--Morrow--Nikolaus. In partially ongoing work with Binda, Merici, and Park, we combine techniques from homotopy theory and logarithmic geometry to generalize these results to the case of semistable special fiber. If time permits, I will highlight some curious aspects of the proof.