I will tell you a story about the Reciprocity Law. After my thesis, I had the idea to define $latex {L}&fg=000000$-series for non-abelian extensions. But for them to agree with the $latex {L}&fg=000000$-series for abelian extensions, a certain isomorphism had to be true. I could show it implied all the standard reciprocity laws. So I… Continue reading Artin Reciprocity