2015/10/20 by Kim, Minhyong · 1 citation
#11G40 #14G10 #81T45 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1510.05818
In this paper, we apply ideas of Dijkgraaf and Witten on 2+1 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 functionals on spaces of Galois representations. In the highly speculative section 5, we consider the far-fetched possibility of using Chern-Simons theory to construct L-functions.