Associated sheaf functors in tensor triangular geometry

Rowe, James Cameron (2023) Associated sheaf functors in tensor triangular geometry. PhD thesis, University of Glasgow.

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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. When the tensor triangulated structure is replaced with a monoidal triangulated structure we show that one can form localising bimodules and central idempotents given particular localisation sequences. Finally, we provide a computation of the spectrum for the enveloping algebra of the A₂ quiver and determine that spectrum consists of a single point.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Subjects: Q Science > QA Mathematics
Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
Supervisor's Name: Stevenson, Dr. Gregory and Muthiah, Dr. Dinakar
Date of Award: 2023
Depositing User: Theses Team
Unique ID: glathesis:2023-83497
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 22 Mar 2023 16:32
Last Modified: 23 Mar 2023 11:20
Thesis DOI: 10.5525/gla.thesis.83497

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