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Questions concerning Brauer groups of fields, rings, varieties, schemes or more general ringed spaces, invariants associated to Brauer classes such as index and period.
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How do Brauer groups relate to zeta functions?
The computation of the Brauer group is only the "first half" of class field theory. The main reason one is interested in the Brauer group is that for a finite Galois extension $L/K$, let's say of loca …