Work

$$\mathbb {A}^1$$-homotopy theory of log schemes

Year: 2026

Type: article

Abstract: We construct the $$\mathbb {A}^1$$ A 1 -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 that our construction satisfies the localization property. As a consequence, we obtain the Grothendieck six-functor formalism for strict morphisms of fs log schemes. We extend $$\mathbb {A}^1$$ A 1 -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.

Source: European Journal of Mathematics

DOI: 10.1007/s40879-026-00916-2

Author: Doosung Park

Institution: University of Wuppertal

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,490

Funder: Deutsche Forschungsgemeinschaft