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arXiv · 1706.03291

On the surjectivity of the map of spectra associated to a tensor-triangulated functor

Paul Balmer
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Abstract

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.

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Paul Balmer. 2017-06-11. On the surjectivity of the map of spectra associated to a tensor-triangulated functor. https://doi.org/10.1112/blms.12158

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