论文标题
$ \ mathbb {a}^1 $ - 原理理论的日志方案
$\mathbb{A}^1$-homotopy theory of log schemes
论文作者
论文摘要
我们构建了$ \ mathbb {a}^1 $ - 局部稳定的动机同型类别FS日志方案。对于具有琐碎日志结构的方案，我们的构建等同于Morel-Voevodsky的原始结构。我们证明了本地化属性。结果，我们获得了Grothendieck六个功能孔形式主义，以实现FS日志方案的严格形式。我们将$ \ mathbb {a}^1 $ - invariant共同体学理论扩展到FS日志方案。特别是，我们定义了动机共同体，同型$ k $ - 理论和FS日志方案的代数COBORDISM。对于任何FS日志方案对方案的平滑日志，我们就方案的共同体学表达了其边界的共同点。
We construct the $\mathbb{A}^1$-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 the localization property. As a consequence, we obtain the Grothendieck six functors formalism for strict morphisms of fs log schemes. We extend $\mathbb{A}^1$-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.
