We prove the Mirković–Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers. (Juteau has exhibited counterexamples when p is a bad prime.) The main idea is to convert this topological question into an algebraic question about perverse-coherent sheaves on the dual nilpotent cone using the Juteau–Mautner–Williamson theory of parity sheaves.

中文翻译：

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仿射 Grassmannian 和 Mirković-Vilonen 猜想的奇偶层

我们证明了 Mirković-Vilonen 猜想：仿射格拉斯曼函数上球形舒伯特变体的积分局部交上同调群没有 p 扭转，只要 p 位于某个小的且明确给定的素数集之外。（当 p 是坏素数时，Juteau 展示了反例。）主要思想是使用 Juteau-Mautner-Williamson 奇偶滑轮理论将这个拓扑问题转换为关于对偶幂零锥上的逆相干滑轮的代数问题。