论文标题
各向同性稳定的动机同型球体
Isotropic stable motivic homotopy groups of spheres
论文作者
论文摘要
在本文中，我们通过杀死各向异性品种，探讨了从通常稳定的动机同型类别构建的各向同性稳定的动机同型类别（参见Vishik在各向同性动机上的工作（见[29]）。特别是，我们专注于各向同性领域中的共同体运营，并研究各向同性steenrod代数的结构。然后，我们构建了动机ADAMS光谱序列的各向同性版本，并将其应用以找到球形光谱的各向同性稳定同型组的完整描述，这些谱谱恰好是拓扑steenrod algebra的$ ext $ groups的同构。最后，我们将看到，这种同构不仅是加性的，而且尊重更高的产品，完全识别出具有较高结构的环，是经典的steenrod代数的共同体，具有各向同性稳定的球体均匀的同型。
In this paper we explore the isotropic stable motivic homotopy category constructed from the usual stable motivic homotopy category, following the work of Vishik on isotropic motives (see [29]), by killing anisotropic varieties. In particular, we focus on cohomology operations in the isotropic realm and study the structure of the isotropic Steenrod algebra. Then, we construct an isotropic version of the motivic Adams spectral sequence and apply it to find a complete description of the isotropic stable homotopy groups of the sphere spectrum, which happen to be isomorphic to the $Ext$-groups of the topological Steenrod algebra. At the end, we will see that this isomorphism is not only additive but respects higher products, completely identifying, as rings with higher structure, the cohomology of the classical Steenrod algebra with isotropic stable homotopy groups of spheres.
