Examples of étale extensions of Green functors

Proceedings of the American Mathematical Society, Series B Pub Date : 2024-07-01 DOI:10.1090/bproc/189

A. Lindenstrauss, Birgit Richter, Foling Zou

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引用次数: 1

Abstract

We provide new examples of étale extensions of Green functors by transferring classical examples of étale extensions to the equivariant setting. Our examples are Tambara functors, and we prove Green étaleness for them, which implies Tambara étaleness. We show that every C 2 C_2 -Galois extensions of fields gives rise to an étale extension of C 2 C_2 -Green functors. Here we associate the constant Tambara functor to the base field and the fix-Tambara functor to the extension. We also prove that all C n C_n -Kummer extensions give rise to étale extensions for arbitrary finite n n . Étale extensions of fields induce étale extension of G G -Green functors for any finite group G G by passing to the corresponding constant G G -Tambara functors.

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格林函数的埃塔尔扩展实例

我们通过将经典的等价扩展范例转移到等价环境，提供了格林函子等价扩展的新范例。我们的例子是坦巴拉函子，我们证明了它们的格林常数，这意味着坦巴拉常数。我们证明了场的每个 C 2 C_2 -伽罗瓦扩展都会引起 C 2 C_2 -格林函子的等价扩展。在这里，我们把恒定坦巴拉函子与基域联系起来，把固定坦巴拉函子与扩展联系起来。我们还证明，对于任意有限 n n，所有 C n C_n -库默扩展都会产生 étale 扩展。对于任意有限群 G G，通过传递到相应的恒定 G G -Tambara 函数，场的Étale扩展会引起 G G -Green 函数的Étale扩展。

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来源期刊

Proceedings of the American Mathematical Society, Series B

CiteScore

1.60

自引率

0.00%

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