On surjectivity in tensor triangular geometry

Tobias Barthel; Natalia Castellana; Drew Heard; Beren Sanders

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arXiv · 2305.05604

On surjectivity in tensor triangular geometry

Tobias Barthel·Natalia Castellana·Drew Heard·Beren Sanders

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Abstract

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.

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BibTeX RIS

Tobias Barthel, Natalia Castellana, Drew Heard, Beren Sanders. 2023-05-09. On surjectivity in tensor triangular geometry. https://arxiv.org/abs/2305.05604

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