论文标题
Faisceau Automorphe Uniptent Pour $ \ Mathrm G_2 $，Nombres de Franel等分层de Thom-Boardman
Faisceau Automorphe Unipotent pour $\mathrm G_2$, Nombres de Franel, et Stratification de Thom-Boardman
论文作者
论文摘要
我们概括了J. Denef和F. loeser关于Tori上的三角分支的结果；另一方面，我们研究了与曲线上线束的全局部分相关的Thom-BoardMan分层。我们证明了这些地层的维度微妙的不等式。我们的动机来自几何兰兰兹计划。根据W. T. Gan，N。Gurevich，D。Jiang和S. Lysenko的作品，我们建议为$ \ Mathrm G_2 $的还原组$ g $ G $，这是一种自以为是的Arthur参数的自以为是的构造，其Arthur参数是无与伦比的，并且是尺寸的。使用上面的两个结果，我们确定了$ s_3 $ - equivAraint sheaf的所有同种型组件的通用等级，该组件出现在我们的猜想中，这$ s_3 $是langlands dual dual of g $ g $ sub-s_3 $。
We generalise to the equivariant case a result of J. Denef and F. Loeser about trigonometric sums on tori; on the other hand, we study the Thom-Boardman stratification associated to the multiplication of global sections of line bundles on a curve. We prove a subtle inequaliity about the dimensions of these strata. Our motivation comes from the geometric Langlands program. Based on works of W. T. Gan, N. Gurevich, D. Jiang and S. Lysenko, we propose, for the reductive group $G$ of type $\mathrm G_2$, a conjectural construction of the automorphic sheaf whose Arthur parameter is unipotent and sub-regular. Using our two results above, we determine the generic ranks of all isotypic components of an $S_3$-equivaraint sheaf which appears in our conjecture, this $S_3$ being the centraliser of the sub-regular $\mathrm{SL}_2$ inside the Langlands dual group of $G$.
