Federico Binda (Milano): On the p-adic deformation of K-theory classes

In this talk I will survey some recent results around generalizations of the Beilinson-Bloch-Esnault-Kerz fiber square, relating the algebraic K-theory of a scheme to its topological cyclic homology. In particular, I will discuss how log geometry naturally enters the picture in the case of bad reduction, and how one can control the obstruction to lifting K-theory classes in the semistable case using the “Hyodo-Kato Chern character”, extending the work of Antieau-Mathew-Morrow-Nikolaus. The methods involve some reduction from the logarithmic to the non logarithmic case, using some results of motivic origin in the non-A^{^1}-invariant setting.

Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)