Logarithmic motivic homotopy theory
Logarithmic motivic homotopy theory
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对数动机同伦理论
DOI：
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
P. Ostvaer
中科院分区：
文献类型：
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作者：
F. Binda;Doosung Park;P. Ostvaer
本文致力于构造一个新的（log）格式的动机同伦理论，推广了Morel-Voevodsky的（不）稳定$\mathbb{A}^1$-同伦范畴.我们的设置可以用来表示日志拓扑Hochschild和循环同调，以及代数$K$-理论的定期计划，并实现分圆迹作为一个态射之间的motivic谱。在应用程序中，一个广义的框架导向上同调理论使我们能够产生新的残留序列（拓扑）Hochschild，周期和循环同源的经典计划，计算$\mathrm{THH}$和变种的格拉斯曼，并定义一个新版本的代数配边。最后，我们给出了一个对数稳定实现函子和一个Kato-Nakayama实现函子的构造，它们在对数几何中的应用是独立的。
This work is dedicated to the construction of a new motivic homotopy theory for (log) schemes, generalizing Morel-Voevodsky's (un)stable $\mathbb{A}^1$-homotopy category. Our setting can be used to represent log topological Hochschild and cyclic homology, as well as algebraic $K$-theory of regular schemes, and to realize the cyclotomic trace as a morphism between motivic spectra. Among the applications, a generalized framework of oriented cohomology theories allows us to produce new residue sequences for (topological) Hochschild, periodic and cyclic homology of classical schemes, to compute $\mathrm{THH}$ and variants of Grassmannians, and to define a new version of algebraic cobordism. Finally, we give a construction of a log \'etale stable realization functor, as well as a Kato-Nakayama realization functor, which are of independent interest for applications in log geometry.