A Statistical Approach to the Global Artin Reciprocity Map: An Unconditional Non-abelian Global Class Field Theory

Abstract: In this talk, borrowing tools from statistics, we shall first construct, following T. Ono, an unconditional non-Abelian generalization of the global Artin reciprocity map for any finite Galois extension $\mathbf{E}$ of a global field $\mathbf{F}$. This theory has deep connections with the Langlands reciprocity principle, while the latter is still conjectural. In the second part of the talk, we plan to discuss some properties of the Ono reciprocity map for $\mathbf{E}/\mathbf{F}$, and construct the (absolute) Ono reciprocity map for $\mathbf{F}^{sep}/\mathbf{F}$. Finally, we plan to give a description of the maximal unramified extension of $\mathbf{F}$ inside $\mathbf{F}^{sep}$, which is closely related with the Golod-Shafarevich Theory. This is joint work with my PhD student Serkan Kızılavuz (Eskişehir Technical University).

Mathematics

Audience: researchers in the topic

METU Mathematics General Seminar