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- W3096606962 abstract "In this expository paper we provide a geometric proof of the local Langlands Correspondence for the groups $operatorname{GL}_{1}$ defined over $p$-adic fields $K$. We do this by redeveloping the theory of proalgebraic groups and use this to derive local class field theory in the style of Serre and Hazewinkel. In particular, we show that the local class field theory of Serre and Hazewinkel is valid for both equal characteristic and mixed characteristic ultrametric local fields. Finally, we use this to prove an equivalence of the categories of smooth representations of $K^{ast}$ with continuous representations of $W_K^{text{Ab}}$ in order to deduce the Local Langlands Correspondence for $operatorname{GL}_{1,K}$." @default.
- W3096606962 created "2020-11-09" @default.
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- W3096606962 date "2020-10-30" @default.
- W3096606962 modified "2023-09-27" @default.
- W3096606962 title "Serre-Hazewinkel Local Class Field Theory and a Geometric Proof of the Local Langlands Correspondence for $operatorname{GL}(1)$" @default.
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