Serre-Hazewinkel Local Class Field Theory and a Geometric Proof of the Local Langlands Correspondence for $\mathrm{GL}(1)$

Geoff Vooys

In this expository paper we provide a geometric proof of the local Langlands Correspondence for the groups ${\mathrm{GL}}_1$ defined over $p$-adic fields $K$. We do this by r…