论文标题
Aggine Mod $ p $ hecke代数中的中心元素通过oververse $ \ mathbb {f} _p $ -sheaves
Central elements in affine mod $p$ Hecke algebras via perverse $\mathbb{F}_p$-sheaves
论文作者
论文摘要
令$ g $为特征性$ p> 2 $的有限字段，使得$ g_ \ text {der} $几乎是绝对简单的。我们在iWahori affine Flag品种$ g $的$ G $上提供了不正当$ \ Mathbb {f} _p $ -sheave的几何结构，这对于卷积产品至关重要。我们从球形mod $ p $ hecke代数到Iwahori mod mod $ p $ p $ hecke代数的同构的明确公式。我们还为Iwahori mod $ p $ hecke代数的中央积分伯恩斯坦元素提供了一个公式。为了实现这些目标，我们构建了一个附近的循环函数，以实现不错的$ \ mathbb {f} _p $ -sheaves，我们使用Frobenius拆分技术来证明该函数的某些属性。我们还证明，Shimura品种本地模型的某些同等特征类似物非常强烈，因此它们是$ f $ - 理性的，并且具有伪理性的奇迹。
Let $G$ be a split connected reductive group over a finite field of characteristic $p > 2$ such that $G_\text{der}$ is absolutely almost simple. We give a geometric construction of perverse $\mathbb{F}_p$-sheaves on the Iwahori affine flag variety of $G$ which are central with respect to the convolution product. We deduce an explicit formula for an isomorphism from the spherical mod $p$ Hecke algebra to the center of the Iwahori mod $p$ Hecke algebra. We also give a formula for the central integral Bernstein elements in the Iwahori mod $p$ Hecke algebra. To accomplish these goals we construct a nearby cycles functor for perverse $\mathbb{F}_p$-sheaves and we use Frobenius splitting techniques to prove some properties of this functor. We also prove that certain equal characteristic analogues of local models of Shimura varieties are strongly $F$-regular, and hence they are $F$-rational and have pseudo-rational singularities.
