Construction of logarithmic cohomology theories I

2025/03/02 by Park, Doosung · 2 citations
#14A21 #14F42 #14M25 #19D55 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2503.01043

Abstract

We propose a method for constructing cohomology theories of logarithmic schemes with strict normal crossing boundaries by employing techniques from logarithmic motivic homotopy theory over \mathbbF₁. This method recovers the K-theory of the open complement of a strict normal crossing divisor from the K-theory of schemes as well as logarithmic topological Hochschild homology from the topological Hochschild homology of schemes. In our applications, we establish that the K-theory of non-regular schemes is representable in the logarithmic motivic homotopy category, and we introduce the logarithmic cyclotomic trace for the regular log regular case.

Cited by

• Log syntomic cohomology of truncated polynomials and coordinate axes
• On the Residue Sequence in Logarithmic Topological Cyclic Homology

Related

• Logarithmic motivic homotopy theory
• \mathbbA¹-homotopy theory of log schemes
• Triangulated categories of logarithmic motives over a field
• Logarithmic motives with compact support
• Logarithmic Gysin sequences for regular immersions