2016/09/10 by Chung, Hee-Joong, Kim, Dohyeong, Kim, Minhyong +2 · 1 citation
#11R04 #11R23 #11R29 #81T45 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1609.03012
We apply ideas of Dijkgraaf and Witten on three-dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields. In the first three sections, we define classical Chern-Simons actions on spaces of Galois representations. In the subsequent sections, we give formulas for computation in a small class of cases and point towards some arithmetic applications.