We provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category, where the tensor product is not necessarily symmetric. This is illustrated by examples, taken in particular from representation theory of finite dimensional algebras.
Funding
The authors thank the Mathematisches Forschungsinstitut Oberwolfach for the unique
opportunity and for the support of our two Research in Pairs stays in 2002 and 2004, which made this work
possible.