UCLA

We consider separable ring objects in symmetric monoidal categories and investigate what it means for an extension of ring objects to be (quasi)-Galois. Reminiscent of field theory, we define splitting ring extensions and examine how they occur. We also establish a version of quasi-Galois-descent for ring objects.

Specializing to tensor-triangulated categories, we study how extension-of-scalars along a quasi-Galois ring object affects the Balmer spectrum. We define what it means for a separable ring to have constant degree, which turns out to be a necessary and sufficient condition for the existence of a quasi-Galois closure. Finally, we illustrate the above for separable rings occurring in modular representation theory.