论文标题
雅各布森 - 兰格兰在相对环境中参数的morozov形态
The Jacobson--Morozov morphism for Langlands parameters in the relative setting
论文作者
论文摘要
我们构建一个模量空间$ \ mathsf {lp} _g $ of $ \ mathrm {sl} _2 $ - parameters $ \ mathbb {q} $，并证明其具有良好的几何属性（例如，明确具有参数化的几何相关的组件和平滑度）。我们构造了一个jacobson- morozov形态$ \ MATHSF {JM} \ COLON \ MATHSF {lp} _G \ to \ Mathsf {wdp} _g $（其中$ \ Mathsf {wdp} _g $是Weiliiligne的模块化空间。我们表明，$ \ mathsf {jm} $是$ \ mathsf {wdp} _g $的密集开放的同构，它诱导了离散基因座之间的同构美元$ \ mathsf {lp} _g（a）$和frobenius semi-simple等价类中的$ \ mathsf {wdp} _g（a）$，带有常数（与共轭）单片操作员。
We construct a moduli space $\mathsf{LP}_G$ of $\mathrm{SL}_2$-parameters over $\mathbb{Q}$, and show that it has good geometric properties (e.g. explicitly parametrized geometric connected components and smoothness). We construct a Jacobson--Morozov morphism $\mathsf{JM}\colon \mathsf{LP}_G\to\mathsf{WDP}_G$ (where $\mathsf{WDP}_G$ is the moduli space of Weil--Deligne parameters considered by several other authors). We show that $\mathsf{JM}$ is an isomorphism over a dense open of $\mathsf{WDP}_G$, that it induces an isomorphism between the discrete loci $\mathsf{LP}^{\mathrm{disc}}_G\to\mathsf{WDP}_G^{\mathrm{disc}}$, and that for any $\mathbb{Q}$-algebra $A$ it induces a bijection between Frobenius semi-simple equivalence classes in $\mathsf{LP}_G(A)$ and Frobenius semi-simple equivalence classes in $\mathsf{WDP}_G(A)$ with constant (up to conjugacy) monodromy operator.
