On surjectivity in tensor triangular geometry
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866910620444524544 |
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| author | Barthel, Tobias Castellana, Natalia Heard, Drew Sanders, Beren |
| author_facet | Barthel, Tobias Castellana, Natalia Heard, Drew Sanders, Beren |
| contents | We prove that a jointly conservative family of geometric functors between rigidly-compactly generated tensor triangulated categories induces a surjective map on Balmer spectra. From this we deduce a fiberwise criterion for Balmer's comparison map to be a continuous bijection. This gives short alternative proofs of the Hopkins--Neeman theorem and its generalization, due to Lau, to the case of a finite group acting trivially on an affine scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_05604 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On surjectivity in tensor triangular geometry Barthel, Tobias Castellana, Natalia Heard, Drew Sanders, Beren Category Theory Algebraic Topology Representation Theory We prove that a jointly conservative family of geometric functors between rigidly-compactly generated tensor triangulated categories induces a surjective map on Balmer spectra. From this we deduce a fiberwise criterion for Balmer's comparison map to be a continuous bijection. This gives short alternative proofs of the Hopkins--Neeman theorem and its generalization, due to Lau, to the case of a finite group acting trivially on an affine scheme. |
| title | On surjectivity in tensor triangular geometry |
| topic | Category Theory Algebraic Topology Representation Theory |
| url | https://arxiv.org/abs/2305.05604 |