8 papers
A construction of tame sheaves and tame de Rham--Witt cohomology
Alberto Merici, Kay Rülling, Shuji Saito
In this article, we consider an algebraic version of the tame site of a pair . With this definition, we provide a general machinery to construct a tame sheaf fro…
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…
Birational and -invariant lattices in the cohomology of the structure sheaf over non-archimedean fields
Alberto Merici, Kay Rülling, Shuji Saito
We show that the cohomology of the structure sheaf of smooth and proper schemes over a complete non-archimedean field of characteristic zero, can be refined to an $\mathbf{A}^1…
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…
Some computations in the heart of the homotopy t-structure on logarithmic motives
Alberto Merici
In this note we will illustrate a method for computing the of the effective log motive of a smooth and proper variety over a perfect field and show that it is $\mathbf{A…
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…