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Galois and separable extensions of Tambara functors
Abstract
For a map of Tambara functors R → T we define when T is separable over R and if T carries an action by some finite group H that fixes R we also define when R → T is an H-Galois extension of Tambara functors. We show that flat and separable extensions are (formally) étale in the sense of Hill and that Galois extensions are separable. We prove that the Burnside Tambara functor is separably closed and we express Nullstellensatzian Tambara functors as filtered colimits of Galois extensions.
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BibTeX
@misc{richter2026galois,
title = {{Galois and separable extensions of Tambara functors}},
author = {Birgit Richter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.04411},
eprint = {2607.04411},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04411},
}
RIS
TY - UNPB
TI - Galois and separable extensions of Tambara functors
AU - Birgit Richter
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2607.04411
UR - https://arxiv.org/abs/2607.04411
AB - For a map of Tambara functors R → T we define when T is separable over R and if T carries an action by some finite group H that fixes R we also define when R → T is an H-Galois extension of Tambara functors. We show that flat and separable extensions are (formally) étale in the sense of Hill and that Galois extensions are separable. We prove that the Burnside Tambara functor is separably closed and we express Nullstellensatzian Tambara functors as filtered colimits of Galois extensions.
ER -