Kummer theory provides a way of recognizing the isomorphism classes of (certain) Galois extensions of fields containing enough roots of unity. Running a similar machinery for general classical commutative rings leads to the classification of (certain) Galois extensions of the ring which involves the Picard spectrum of the ring. Schlank, et al. have designed a version of this theory that works for nice presentable additive symmetric monoidal ∞-categories which involves the Picard spectrum of this category. I will go over their version of the theory in this talk.
