PUB - Publikationen an der Universität Bielefeld

For a tensor-triangulated category and any regular cardinal alpha$\alpha$, we study the frame of alpha$\alpha$-localizing tensor ideals and its associated space of points. For a well-generated category and its frame of localizing tensor ideals, we provide conditions such that the associated space is obtained by refining the topology of the corresponding space for the triangulated subcategory of alpha$\alpha$-compact objects. This is illustrated by several known examples for alpha=aleph 0$\alpha =\aleph _0$, and new spaces arise for alpha>aleph 0$\alpha >\aleph _0$.