Examples of étale extensions of Green functors
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917702037143552 |
|---|---|
| author | Lindenstrauss, Ayelet Richter, Birgit Zou, Foling |
| author_facet | Lindenstrauss, Ayelet Richter, Birgit Zou, Foling |
| contents | 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 $C_2$-Galois extensions of fields gives rise to an étale extension of $C_2$-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 $C_n$-Kummer extensions give rise to étale extensions for arbitrary finite $n$. Étale extensions of fields induce étale extension of $G$-Green functors for any finite group $G$ by passing to the corresponding constant $G$-Tambara functors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01656 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Examples of étale extensions of Green functors Lindenstrauss, Ayelet Richter, Birgit Zou, Foling Algebraic Topology Commutative Algebra 55P91, 13B40 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 $C_2$-Galois extensions of fields gives rise to an étale extension of $C_2$-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 $C_n$-Kummer extensions give rise to étale extensions for arbitrary finite $n$. Étale extensions of fields induce étale extension of $G$-Green functors for any finite group $G$ by passing to the corresponding constant $G$-Tambara functors. |
| title | Examples of étale extensions of Green functors |
| topic | Algebraic Topology Commutative Algebra 55P91, 13B40 |
| url | https://arxiv.org/abs/2304.01656 |