Konrad Bals | Searcharxiv

arXiv2024

The Topological Cartier--Raynaud Ring

We prove that the $\infty$-category of $p$-typical topological Cartier modules, recently introduced by Antieau--Nikolaus, over some base $A$ is equivalent to the $\infty$-category of modules over a ring spectrum $\mathcal R_A$, which we call the topological Cartier--Raynaud ring. Our main result is an identification of the homotopy groups of $\mathcal R_A$. In particular, for $A=W(k)$, the Witt vectors over $k$, the homotopy groups $π_*\mathcal R_{W(k)}$ recover the classical Cartier--Raynaud ring constructed by Illusie--Raynaud. Moreover, along the way we will describe the compact generator of $p$-typical topological Cartier modules and classifies all natural operations on homotopy groups of $p$-typical topological Cartier modules.

math.AT↗

arXiv2023

Periodic Cyclic Homology over Q

Let $X$ be a derived scheme over an animated commutative ring of characteristic 0. We give a complete description of the periodic cyclic homology of $X$ in terms of the Hodge completed derived de Rham complex of $X$. In particular this extends earlier computations of Loday-Quillen to non-smooth algebras. Moreover, we get an explicit condition on the Hodge completed derived de Rham complex, that makes the HKR-filtration on periodic cyclic homology constructed by Antieau and Bhatt-Lurie exhaustive.

math.AT↗