论文标题
Whittaker功能是移动的微音
The Whittaker functional is a shifted microstalk
论文作者
论文摘要
对于光滑的投影曲线$ x $和还原组的$ g $，惠特克在$ \ text {bun} _g（x）$上的Nilpotent Sheaves上有望对应于Betti几何灯园的光谱侧面的全球连贯吊带束。我们证明，惠特克功能性计算了nilpotent滑轮的（移动的）微骨位于Hitchin模量的点，而Kostant截面与全局nilpotent锥相交。特别是，（移动的）Whittaker功能是正确的$ t $结构，并使用Verdier二元性通勤。我们的证明是拓扑的，取决于$ \ text {bun} _g（x）$的内在局部双曲线对称性。它是将消失的周期与限制与吸引基因座的组成有关的一般结果的应用。
For a smooth projective curve $X$ and reductive group $G$, the Whittaker functional on nilpotent sheaves on $\text{Bun}_G(X)$ is expected to correspond to global sections of coherent sheaves on the spectral side of Betti geometric Langlands. We prove that the Whittaker functional calculates the (shifted) microstalk of nilpotent sheaves at the point in the Hitchin moduli where the Kostant section intersects the global nilpotent cone. In particular, the (shifted) Whittaker functional is exact for the perverse $t$-structure and commutes with Verdier duality. Our proof is topological and depends on the intrinsic local hyperbolic symmetry of $\text{Bun}_G(X)$. It is an application of a general result relating vanishing cycles to the composition of restriction to an attracting locus followed by vanishing cycles.
