We take a direct approach to computing the orbits for the action of the automorphism group \(\mathbb {G}_2\) of the Honda formal group law of height 2 on the associated Lubin–Tate rings \(R_2\). We prove that \((R_2/p)_{\mathbb {G}_2} \cong \mathbb {F}_p\). The result is new for \(p=2\) and \(p=3\). For primes \(p\ge 5\), the result is a consequence of computations of Shimomura and Yabe and has been reproduced by Kohlhaase using different methods.

中文翻译：

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鲁宾-泰特环的轨道计算

我们采用一种直接方法来计算相关Lubin–Tate环\（R_2 \）上本田形式群定律2的自同构群\（\ mathbb {G} _2 \）的作用的轨道。我们证明\（（R_2 / p）_ {\ mathbb {G} _2} \ cong \ mathbb {F} _p \）。结果是\（p = 2 \）和\（p = 3 \）的新结果。对于素数\（p \ ge 5 \），结果是Shimomura和Yabe计算得出的结果，由Kohlhaase使用不同的方法进行了重现。