Local Bousfield classes

In this project we study homological and cohomological Bousfield classes in Bousfield localizations of rigidly-compactly generated tensor–triangulated categories. They are special classes of localizing ideals and we investigate its classification via the homological spectrum introduced by Balmer in the context of tt-geometry. In the case of chromatic homotopy theory, we provide examples of cohomological Bousfield classes which are not homological. This joint work with T. Barthel, D. Heard, B. Sanders and C. Zou.