Abstract
Given a ring object in a symmetric monoidal category, we investigate what it means for the extension to be (quasi-)Galois. In particular, we define splitting ring extensions and examine how they occur. 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 is 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.
Citation
Bregje Pauwels. "Quasi-Galois theory in symmetric monoidal categories." Algebra Number Theory 11 (8) 1891 - 1920, 2017. https://doi.org/10.2140/ant.2017.11.1891
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