We discuss support variety theory for quasireductive algebraic supergroups, i.e. supergroups with reductive even part over complex numbers. The corresponding categories of representations are Frobenius and share many properties of representations of finite groups in positive characteristic. It is desirable to describe Balmer spectrum of related triangulated symmetric monoidal categories. Our approach involves so called homological odd elements and certain tensor functors associated to them. On the way we encounter analogues of p-groups and Sylow subgroups for supergroups. We prove projectivity detection for our support theory and present other related results. We also explore connections with homological support theory developed by B. Boe, J. Kujawa and D. Nakano.
This talk is based on joint work with J. Pevtsova, A. Sherman and D. Vaintrob.
This video is part of the conference Representation Theory and Geometry that took place at the University of Georgia.
