论文标题
mod- $ p $ toplectic蒙特利尔函数
A mod-$p$ metaplectic Montréal functor
论文作者
论文摘要
我们将Colmez的函子定义为$ \ operatorname {gl} _2（\ Mathbf {q} _p）$，以置于有限生成的平稳生成的平滑可容纳的可允许的mod- $ p $表示$ \ perperatornAme {gl} _2} _2 _2 _2 _2（\ mathbff ply）的两倍的替代封面的表示。我们计算绝对不可还原的真实物体的图像，并在真正的超级表现形式和四维不可约的galois表示之间获得双重态度。扩展函子仅限于真正的对象，自然地将值列为我们所谓的元容器galois表示的类别 - 带有一定额外结构编码上述扭转不变性的galois表示。
We extend Colmez's functor defined for $\operatorname{GL}_2(\mathbf{Q}_p)$ to the category of finitely generated smooth admissible mod-$p$ representations of the two-fold metaplectic cover of $\operatorname{GL}_2(\mathbf{Q}_p)$. We compute the images of the absolutely irreducible genuine objects and obtain a bijection between the genuine supersingular representations and four-dimensional irreducible Galois representations invariant under twist by all characters of order two. Restricted to genuine objects, the extended functor naturally takes values in the category of what we call metaplectic Galois representations -- Galois representations with a certain extra structure encoding the aforementioned twist-invariance.
