1. The spectrum of a well‐generated tensor‐triangulated category
- Author
-
Krause, Henning and Letz, Janina C.
- Subjects
Mathematics::Logic ,Mathematics - Algebraic Geometry ,Mathematics::Category Theory ,18G80 (primary), 18F70, 18C35 (secondary) ,General Mathematics ,FOS: Mathematics ,Category Theory (math.CT) ,Mathematics - Category Theory ,Representation Theory (math.RT) ,Algebraic Geometry (math.AG) ,Mathematics - Representation Theory - Abstract
For a tensor triangulated category and any regular cardinal $\alpha$ we study the frame of $\alpha$-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 $\alpha$-compact objects. This is illustrated by several known examples for $\alpha=\aleph_0$, and new spaces arise for $\alpha>\aleph_0$., Comment: 20 pages. Revisions. To appear in Bulletin of the London Mathematical Society
- Published
- 2022