论文标题
迈向$ \ gl_2 $在完全真实领域的mod- $ p $ lubin-tate理论
Towards a mod-$p$ Lubin-Tate theory for $\GL_2$ over totally real fields
论文作者
论文摘要
我们表明，可以在Lubin-Tate Towers的Mod $ p $共同体中实现猜想的Mod $ P $本地Langlands通信。该证明利用了众所周知的buzzard-diamond-jarvis \ cite [conj。 4.9] {bdj10}，一项针对Shimura曲线的普通和超级分子的共同体学的研究，用于完全真实的领域$ f $和mod $ l（\ neq p）$ local langlands对应关系，如emerton-helm \ cite {emertonhelm14}。 ％，然后我们将完整的同胞与卢宾塔塔的共同体相关联。在模块化曲线的情况下，Chojecki \ cite {cho15}获得了类似的定理。
We show that the conjectural mod $p$ local Langlands correspondence can be realised in the mod $p$ cohomology of the Lubin-Tate towers. The proof utilizes a well known conjecture of Buzzard-Diamond-Jarvis \cite[Conj. 4.9]{BDJ10}, a study of completed cohomology of the ordinary and supersingular locus of the Shimura curves for a totally real field $F$ and of mod $l(\neq p)$ local Langlands correspondence as given by Emerton-Helm \cite{EmertonHelm14}. %And then we connect the completed cohomlgy with the cohomology of Lubin-Tate towers. In the case of modular curves a similar theorem was obtained by Chojecki \cite{Cho15}.
