Associated sheaf functors in tt-geometry

James Rowe

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arXiv · 2111.06233

Associated sheaf functors in tt-geometry

James Rowe

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Abstract

Given a tensor triangulated category we investigate the geometry of the Balmer spectrum as a locally ringed space. Specifically we construct functors assigning to every object in the category a corresponding sheaf and a notion of support based upon these sheaves. We compare this support to the usual support in tt-geometry and show that under reasonable conditions they agree on compact objects. We show that when tt-categories satisfy a scheme-like property then the sheaf associated to an object is quasi-coherent, and that in the presence of an appropriate t-structure and affine assumption, this sheaf is in fact the sheaf associated to the object's zeroth cohomology.

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BibTeX RIS

James Rowe. 2021-11-11. Associated sheaf functors in tt-geometry. https://arxiv.org/abs/2111.06233

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