2021/11/11 by Rowe, James
#18G80 (Primary) 18F99 (Secondary) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2111.06233
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.