标题： 伯科维奇动机 显示英文标题

标题： Berkovich Motives

摘要： 我们构建了一个关于（étale）Berkovich动机的理论。 这个理论与Ayoub的刚性解析动机理论密切相关，但在阿基米德和非阿基米德情形下都能统一工作。 我们的目标是提供一个自洽的处理方法，不依赖于之前关于代数或解析动机的工作。 将该理论应用于离散域时，仍可以恢复Voevodsky理论的étale版本。 我们的设定中有两个显著特征，在其他设定中并不成立：首先，在任意基上，消减定理均成立；其次，在对基施加轻微假设的情况下，动机层的稳定$\infty$- 范畴是刚性对偶化的。 显示英文摘要

摘要： We construct a theory of (etale) Berkovich motives. This is closely related to Ayoub's theory of rigid-analytic motives, but works uniformly in the archimedean and nonarchimedean setting. We aim for a self-contained treatment, not relying on previous work on algebraic or analytic motives. Applying the theory to discrete fields, one still recovers the etale version of Voevodsky's theory. Two notable features of our setting which do not hold in other settings are that over any base, the cancellation theorem holds true, and under only minor assumptions on the base, the stable $\infty$-category of motivic sheaves is rigid dualizable.