标题： 带有分歧滤链的动机同伦理论 显示英文标题

标题： Motivic homotopy theory with ramification filtrations

摘要： 本文的目的是连接两个重要且看似无关的理论：动机同伦理论和分歧理论。 我们在一个qcqs基概形$S$上构造了动机同伦范畴，在其中具有分歧滤链的上同调理论是可表示的。 每种这样的上同调理论都具有基本性质，如Nisnevich下降、立方不变性、爆破不变性、光滑爆破切除、Gysin序列、射影丛公式和 Thom 同构。 当$S$是一个完美域的谱时，每个互反层的上同调都被提升为在我们范畴中以分歧滤链表示的上同调理论。 我们还讨论了我们的理论与其他非$\mathbb{A}^1$-不变的动机同伦理论之间的关系，例如 Binda、Park 和{\O }stv{\ae }r 的对数动机同伦理论，以及 Annala-Iwasa 的动机谱理论。 显示英文摘要

摘要： The aim of this paper is to connect two important and apparently unrelated theories: motivic homotopy theory and ramification theory. We construct motivic homotopy categories over a qcqs base scheme $S$, in which cohomology theories with ramification filtrations are representable. Every such cohomology theory enjoys basic properties such as the Nisnevich descent, the cube-invariance, the blow-up invariance, the smooth blow-up excision, the Gysin sequence, the projective bundle formula and the Thom isomorphism. In case $S$ is the spectrum of a perfect field, the cohomology of every reciprocity sheaf is upgraded to a cohomology theory with a ramification filtration represented in our categories. We also address relations of our theory with other non-$\mathbb{A}^1$-invariant motivic homotopy theories such as the logarithmic motivic homotopy theory of Binda, Park, and {\O}stv{\ae}r and the theory of motivic spectra of Annala-Iwasa.