论文标题
mod $ p $ hecke代数的Satake变换的几何化
Geometrization of the Satake transform for mod $p$ Hecke algebras
论文作者
论文摘要
我们使用Witt Vector Aggine Fragine Flag品种用于混合特征的还原群体的Mod $ p $ satake同构同构。我们将其推断为公式的特殊情况，根据广义Mirković-Vilonen循环的几何形状，是关于任意的levi子组的任意偏执mod $ p $ hecke代数的萨克克变换。此外，我们证明了在任意的Parahoric mod $ p $ hecke代数中的卷积产品的明确公式。我们的方法涉及从几何Langlands程序中启发的恒定项函数，我们还以同等特征对待还原基团的情况。我们希望这将是迈向Mod $ p $本地Langlands通信的几何化的第一步。
We geometrize the mod $p$ Satake isomorphism of Herzig and Henniart-Vignéras using Witt vector affine flag varieties for reductive groups in mixed characteristic. We deduce this as a special case of a formula, stated in terms of the geometry of generalized Mirković-Vilonen cycles, for the Satake transform of an arbitrary pararhoric mod $p$ Hecke algebra with respect to an arbitrary Levi subgroup. Moreover, we prove an explicit formula for the convolution product in an arbitrary parahoric mod $p$ Hecke algebra. Our methods involve the constant term functors inspired from the geometric Langlands program, and we also treat the case of reductive groups in equal characteristic. We expect this to be a first step towards a geometrization of a mod $p$ Local Langlands Correspondence.
