Arithmetic Chern-Simons Theory I
Number Theory
2016-11-14 v4 Mathematical Physics
Algebraic Geometry
Algebraic Topology
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1510.05818,
title = {Arithmetic Chern-Simons Theory I},
author = {Minhyong Kim},
journal= {arXiv preprint arXiv:1510.05818},
year = {2016}
}
Comments
with Appendix B by Behrang Noohi. A section added with brief sketch of a glueing formula. Section 3 corrected and simplified