A lower bound for composition multiplicities for the Springer resolution. Issue 11 (2nd November 2018)

• Record Type: Journal Article
• Authors: Shchigolev, Vladimir
• Is Part Of: Communications in algebra. Volume 46:Issue 11(2018)
• Page Start: 4690
• Page End: 4709
• Publication Date: 2018-11-02
• Subjects: Cohomology -- nilpotent cone -- perverse sheaves -- Springer resolution; 55N30 (Sheaf cohomology); Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1455097
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Letπ : 𝒩 ̃ → 𝒩 be the Springer resolution of the nilpotent cone for a semisimple connected algebraic group G over ℂ and k be an arbitrary field. What happens toπ ∗ k ̲ 𝒩 ̃ [ dim 𝒩 ̃ ] if the decomposition theorem fails for it? We show that in this case, some additional (with respect to the case char k =0) composition factors of this direct image in the (abelian) category of perverse sheaves may emerge. These factors emerge from theZ G ( x ) ∕ Z G ( x ) 0 -composition factors of the radicals of certain intersection forms and from that of the top cohomologies of Springer fibres (in the non-semisimple case).