Resumen

We will introduce two types of topological spaces associated to modules and to bimodules for some types of rings, namely the Balmer support and the cohomological support. These spaces can be important tools for understanding the structure of categories of modules and bimodules, and can be defined in a general setting of monoidal triangulated categories. They are understood best in classical settings such as finite group representations. Much is known more generally, while there are still many open questions. We will include some recent results.