Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.07628 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911923678740480 |
|---|---|
| author | Mor, Itamar |
| author_facet | Mor, Itamar |
| contents | Using profinite Galois descent, we compute the Brauer group of the $K(1)$-local category relative to Morava E-theory. At odd primes this group is generated by a cyclic algebra formed using any primitive $(p-1)$st root of unity, but at the prime two is a group of order $32$ with nontrivial extensions; we give explicit descriptions of the generators, and consider their images in the Brauer group of $KO$. Along the way, we compute the relative Brauer group of completed $KO$, using the étale locally trivial Brauer group of Antieau, Meier and Stojanoska. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07628 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The relative Brauer group of $K(1)$-local spectra Mor, Itamar Algebraic Topology 55P42 (Primary) 14F22 (Secondary) Using profinite Galois descent, we compute the Brauer group of the $K(1)$-local category relative to Morava E-theory. At odd primes this group is generated by a cyclic algebra formed using any primitive $(p-1)$st root of unity, but at the prime two is a group of order $32$ with nontrivial extensions; we give explicit descriptions of the generators, and consider their images in the Brauer group of $KO$. Along the way, we compute the relative Brauer group of completed $KO$, using the étale locally trivial Brauer group of Antieau, Meier and Stojanoska. |
| title | The relative Brauer group of $K(1)$-local spectra |
| topic | Algebraic Topology 55P42 (Primary) 14F22 (Secondary) |
| url | https://arxiv.org/abs/2310.07628 |