2022/05/29 by Doosung Park, Park, Doosung
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2205.14750
We construct the \mathbbA1-local stable motivic homotopy categories of fs log schemes. For schemes with the trivial log structure, our construction is equivalent to the original construction of Morel-Voevodsky. We prove the localization property. As a consequence, we obtain the Grothendieck six functors formalism for strict morphisms of fs log schemes. We extend \mathbbA1-invariant cohomology theories of schemes to fs log schemes. In particular, we define motivic cohomology, homotopy K-theory, and algebraic cobordism of fs log schemes. For any fs log scheme log smooth over a scheme, we express cohomology of its boundary in terms of cohomology of schemes.