Abstract:We compute the $C_p$-equivariant dual Steenrod algebras associated to the constant Mackey functors $\underline {\mathbb {F}}_p$ and $\underline {\mathbb {Z}}_{(p)}$, as $\mathrm {H}\underline {\mathbb {Z}}_{(p)}$-modules. The $C_p$-spectrum $\mathrm {H}\underline {\mathbb {F}}_p \wedge \mathrm {H}\underline {\mathbb {F}}_p$ is not a direct sum of $RO(C_p)$-graded suspensions of $\mathrm {H}\underline {\mathbb {F}}_p$ when $p$ is odd, in contrast with the classical and $C_2$-equivariant dual Steenrod algebras.

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中文翻译：

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关于 𝐶_{𝑝}-等变对偶 Steenrod 代数

摘要：我们计算与常数 Mackey 函子 $\underline {\mathbb {F}}_p$ 和 $\underline {\mathbb {Z}}_{(p)}$ 相关的 $C_p$-等变对偶 Steenrod 代数，作为 $\mathrm {H}\underline {\mathbb {Z}}_{(p)}$-modules。$C_p$-谱 $\mathrm {H}\underline {\mathbb {F}}_p \wedge \mathrm {H}\underline {\mathbb {F}}_p$ 不是 $RO(C_p )$p$ 为奇数时 $\mathrm {H}\underline {\mathbb {F}}_p$ 的分级悬浮，与经典的和 $C_2$-等变的对偶 Steenrod 代数形成对比。

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