论文标题
Galois Artin-Tate $ \ Mathbb {R} $的重建 - 动机光谱
Galois reconstruction of Artin-Tate $\mathbb{R}$-motivic spectra
论文作者
论文摘要
我们解释了如何重建Artin-Tate $ \ Mathbb {r} $的类别 - 动机光谱作为纯粹拓扑$ C_2 $ Equivariant稳定类别的变形。这种变形的特殊纤维是代数，相当于正式组模量堆栈上的$ C_2 $ equivariant或骨的适当类别。因此，我们的结果直接概括了$τ$哲学的合资纤维，后者彻底改变了古典稳定的同型理论。 一个关键的观察是，$ \ mathbb {r} $的Artin-Tate子类别比以前研究的蜂窝子类别更容易理解。特别是，Artin-Tate类别包含$τ$映射的变体，这是蜂窝类别中明显不存在的特征。
We explain how to reconstruct the category of Artin-Tate $\mathbb{R}$-motivic spectra as a deformation of the purely topological $C_2$-equivariant stable category. The special fiber of this deformation is algebraic, and equivalent to an appropriate category of $C_2$-equivariant sheaves on the moduli stack of formal groups. As such, our results directly generalize the cofiber of $τ$ philosophy that has revolutionized classical stable homotopy theory. A key observation is that the Artin-Tate subcategory of $\mathbb{R}$-motivic spectra is easier to understand than the previously studied cellular subcategory. In particular, the Artin-Tate category contains a variant of the $τ$ map, which is a feature conspicuously absent from the cellular category.
