论文标题
Hecke运营商Morava $ e $ - 不同高度的理论
Hecke operators in Morava $E$-theories of different heights
论文作者
论文摘要
在$ n $ th morava $ e $ - 空间理论上，有一种自然的动作是一种Hecke代数$ \ MATHCAL {H} _n $。我们在$ n $ th和$（n+1）$ st morava $ e $ $ - 理论的合并的共同体学理论中构建了Hecke运营商。这些操作是$（n+1）$ st Morava $ e $ $ - 理论中Hecke运营商的自然扩展，它们会在$ N $ n $ n $ n $ n $ th Morava $ e $ e $ $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ e $ theory the hecke algebra $ \ mathcal {h} _ {n+1} $中的作用。我们研究了Hecke代数$ \ Mathcal {h} _n $和$ \ Mathcal {h} _ {n+1} $对$ n $ th morava $ e $ $ - 理论的关系$ \ MATHCAL {H} _n $ -Module结构通过$ \ Mathcal {H} _ {n+1} $ to $ \ MATHCAL {H} _n $的代数同态限制。
There is a natural action of a kind of Hecke algebra $\mathcal{H}_n$ on the $n$th Morava $E$-theory of spaces. We construct Hecke operators in an amalgamated cohomology theory of the $n$th and the $(n+1)$st Morava $E$-theories. These operations are natural extensions of the Hecke operators in the $(n+1)$st Morava $E$-theory, and they induce an action of the Hecke algebra $\mathcal{H}_{n+1}$ on the $n$th Morava $E$-theory of spaces. We study a relationship between the actions of the Hecke algebras $\mathcal{H}_n$ and $\mathcal{H}_{n+1}$ on the $n$th Morava $E$-theory, and show that the $\mathcal{H}_{n+1}$-module structure is obtained from the $\mathcal{H}_n$-module structure by the restriction along an algebra homomorphism from $\mathcal{H}_{n+1}$ to $\mathcal{H}_n$.
