A survey of support theories for Lie superalgebras and finite supergroup schemes

TL;DR

This survey reviews support variety theories for Lie superalgebras and finite supergroup schemes, highlighting developments in both characteristic zero and positive characteristic contexts.

Contribution

It provides a comprehensive overview of existing support theories, emphasizing recent advances and differences across characteristics.

Findings

Support theories in characteristic zero rely on relative Lie superalgebra cohomology.

Positive characteristic support theories have been developed in recent work.

The survey compares and contrasts these theories across different settings.

Abstract

We survey the current state of various support variety theories for Lie superalgebras and finite supergroup schemes. We pay particular attention to the theory in characteristic zero developed by Boe, Kujawa, and Nakano using relative Lie superalgebra cohomology, and to the theory developed in positive characteristic in our previous work.