On the surjectivity of the map of spectra associated to a tensor-triangulated functor
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866913493250211840 |
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| author | Balmer, Paul |
| author_facet | Balmer, Paul |
| contents | We prove a few results about the map $Spc(F)$ induced on tensor-triangular spectra by a tensor-triangulated functor $F$. First, $F$ is conservative if and only if $Spc(F)$ is surjective on closed points. Second, if $F$ detects tensor-nilpotence of morphisms then $Spc(F)$ is surjective on the whole spectrum. In fact, surjectivity of $Spc(F)$ is equivalent to $F$ detecting the nilpotence of some class of morphisms, namely those morphisms which are nilpotent on their cone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1706_03291 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | On the surjectivity of the map of spectra associated to a tensor-triangulated functor Balmer, Paul Category Theory Algebraic Geometry Algebraic Topology 18E30, 14F42, 19K35, 55U35 We prove a few results about the map $Spc(F)$ induced on tensor-triangular spectra by a tensor-triangulated functor $F$. First, $F$ is conservative if and only if $Spc(F)$ is surjective on closed points. Second, if $F$ detects tensor-nilpotence of morphisms then $Spc(F)$ is surjective on the whole spectrum. In fact, surjectivity of $Spc(F)$ is equivalent to $F$ detecting the nilpotence of some class of morphisms, namely those morphisms which are nilpotent on their cone. |
| title | On the surjectivity of the map of spectra associated to a tensor-triangulated functor |
| topic | Category Theory Algebraic Geometry Algebraic Topology 18E30, 14F42, 19K35, 55U35 |
| url | https://arxiv.org/abs/1706.03291 |