论文标题
Milnor-Witt动机
Milnor-Witt Motives
论文作者
论文摘要
我们发展了Milnor-Witt动机和动机共同体的理论。与Voevodsky的动机理论及其动机共同体相比，第一个区别出现在我们对Milnor-Witt有限的对应关系的定义中，其中我们的周期配备了二次形式。这产生了传输的较弱概念和衍生的动机类别，这些类别更接近稳定的方案理论。我们证明了与泰特对象进行张开时的取消定理，我们将Milnor-Witt动机共同体的对角线部分与次要的witt K理论进行了比较，并且我们提供了代表各种动机共同体学的光谱，以$ \ Mathbb {A}}^1 $衍生类别类别或稳定的稳定类别或稳定的同类类别。
We develop the theory of Milnor-Witt motives and motivic cohomology. Compared to Voevodsky's theory of motives and his motivic cohomology, the first difference appears in our definition of Milnor-Witt finite correspondences, where our cycles come equipped with quadratic forms. This yields a weaker notion of transfers and a derived category of motives that is closer to the stable homotopy theory of schemes. We prove a cancellation theorem when tensoring with the Tate object, we compare the diagonal part of our Milnor-Witt motivic cohomology to Minor-Witt K-theory and we provide spectra representing various versions of motivic cohomology in the $\mathbb{A}^1$-derived category or the stable homotopy category of schemes.
