2023/04/04 by Ayelet Lindenstrauss, Lindenstrauss, Ayelet, Birgit Richter +3 · 2 citations
Mathematics · #13B40 #55P91 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2304.01656
openalex publication_date 2023/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 C2-Galois extensions of fields gives rise to an étale extension of C2-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 Cn-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.