The Eilenberg-Moore adjunction in triangulated categories

Paul Balmer
Wednesday, July 24, 2013 - from 11:00 to 12:00
Nature provides an abundance of triangulated categories but it is usually quite difficult to construct new triangulated categories out of old ones, without using models. The most notorious example of such an abstract construction is localization (following Verdier or Bousfield) and this has numerous applications already. However, in equivariant examples, it is quite difficult to pass from the category associated to a group G to the category associated to a subgroup and localization is of no help there. We shall see that the classical construction of Eilenberg-Moore actually solves that problem in the so-called "separable" case, which covers not only Bousfield localization but also restriction to subgroups and much more. We shall then turn to the question of describing the tt-geometry of such Eilenberg-Moore extensions, in the presence of a tensor structure.