We describe some regular behavior in the motivic wedge, which is an infinite family in the cohomology $\mathrm{Ext}_{\mathbf{A}}(\mathbb{M}_2,\mathbb{M}_2)$ of the $\mathbb{C}$-motivic Steenrod algebra. The key tool is to compare motivic computations to classical computations, to $\mathrm{Ext}_{\mathbf{A}(2)}(\mathbb{M}_2,\mathbb{M}_2)$, or to $h_1$-localization of $\mathrm{Ext}_{\mathbf{A}}(\mathbb{M}_2,\mathbb{M}_2)$. We also give two conjectures on the behavior of the families $e_0^tg^k$ and $\Delta h_1 e_0^t g^k$ in $\mathrm{Ext}_{\mathbf{A}}(\mathbb{M}_2,\mathbb{M}_2)$ which raise naturally from the study of the motivic wedge family.

中文翻译：

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$ \ mathbb {C} $-动力Steenrod代数的同调的楔形族

我们描述了动机楔形中的一些常规行为，这是同调的$ \ mathrm {Ext} _ {\ mathbf {A}}（\ mathbb {M} _2，\ mathbb {M} _2）$ $ \ mathbb {C} $动机的Steenrod代数。关键工具是将动机计算与经典计算，$ \ mathrm {Ext} _ {\ mathbf {A}（2）}（\ mathbb {M} _2，\ mathbb {M} _2）$或$进行比较。 $ _1 \ mathrm {Ext} _ {\ mathbf {A}}（\ mathbb {M} _2，\ mathbb {M} _2）$的h_1 $本地化。我们还对$ \ mathrm {Ext} _ {\ mathbf {A}}（\\ mathbb {M}中$ e_0 ^ tg ^ k $和$ \ Delta h_1 e_0 ^ tg ^ k $家庭的行为给出两个猜想_2，\ mathbb {M} _2）$从动机楔形家族的研究中自然产生。