8 papers
On the -adic deformation problem for the -theory of semistable schemes
Federico Binda, Tommy Lundemo, Alberto Merici +1
We establish a semistable generalization of the Beilinson-Bloch-Esnault-Kerz fiber square, relating the algebraic K-theory of a semistable scheme to its logarithmic topological cyc…
On the Residue Sequence in Logarithmic Topological Cyclic Homology
Tommy Lundemo
As a localizing invariant, THH participates in localization sequences of cyclotomic spectra. We resolve a conjecture of Rognes by relating these to residue sequences in logarithmic…
Logarithmic TC via the Infinite Root Stack and the Beilinson Fiber Square
Federico Binda, Tommy Lundemo, Alberto Merici +1
We apply our previous results on ``saturated descent'' to express a wide range of logarithmic cohomology theories in terms of the infinite root stack. Examples include the log cota…
Logarithmic prismatic cohomology, motivic sheaves, and comparison theorems
Federico Binda, Tommy Lundemo, Alberto Merici +1
We prove that (logarithmic) prismatic and (logarithmic) syntomic cohomology are representable in the category of logarithmic motives. As an application, we obtain Gysin maps for pr…
On Deformation Theory in Higher Logarithmic Geometry
Tommy Lundemo
We initiate the study of deformation theory in the context of derived and higher log geometry. After reconceptualizing the "exactification"-procedures in ordinary log geometry in t…
Logarithmic Prismatic Cohomology via Logarithmic THH
Federico Binda, Tommy Lundemo, Doosung Park +1
Inspired by Bhatt-Morrow-Scholze's work on , we define Nygaard-completed log prismatic cohomology based on log topological Hochschild homology via filtrations on log ${\…
A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology
Federico Binda, Tommy Lundemo, Doosung Park +1
This paper incorporates the theory of Hochschild homology into our program on log motives. We discuss a geometric definition of logarithmic Hochschild homology of derived pre-log r…
On the relationship between logarithmic TAQ and logarithmic THH
Tommy Lundemo
We provide a new description of logarithmic topological André-Quillen homology in terms of the indecomposables of an augmented ring spectrum. The new description allows us to inter…