Parity sheaves on the affine Grassmannian and the Mirkovic-Vilonen conjecture

• 成果类型: Article
• 署名作者: Achar, Pramod N.; Rider, Laura
• 署名单位: Louisiana State University System; Louisiana State University; Massachusetts Institute of Technology (MIT)
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-016-0132-6
• 发表日期: 2015
• 页码: 183-216
• 关键词: properly stratified algebras; representation-theory; langlands duality; VARIETIES

摘要

We prove the Mirkovic-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.