Patch-density in tensor-triangular geometry

Paul Balmer; Martin Gallauer

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arXiv · 2503.15274

Patch-density in tensor-triangular geometry

Paul Balmer·Martin Gallauer

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Abstract

The spectrum of a tensor-triangulated category carries a compact Hausdorff topology, called the constructible topology, also known as the patch topology. We prove that patch-dense subsets detect tt-ideals and we prove that any infinite family of tt-functors that detects nilpotence provides such a patch-dense subset. We review several applications and examples in algebra, in topology and in the representation theory of profinite groups.

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Paul Balmer, Martin Gallauer. 2025-03-19. Patch-density in tensor-triangular geometry. https://arxiv.org/abs/2503.15274

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