Purity and decomposition theorems for staggered sheaves

Abstract

Two major results in the theory of l-adic mixed constructible sheaves are the purity theorem (every simple perverse sheaf is pure) and the decomposition theorem (every pure object in the derived category is a direct sum of shifts of simple perverse sheaves). In this paper, we prove analogues of these results for coherent sheaves. Specificially, we work with staggered sheaves, which form the heart of a certain t-structure on the derived category of equivariant coherent sheaves. We prove, under some reasonable hypotheses, that every simple staggered sheaf is pure, and that every pure complex of coherent sheaves is a direct sum of shifts of simple staggered sheaves.

37 pages

References in corpus (6)

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• Complexes d'intersection des compactifications de Baily-Borel. Le cas des groupes unitaires sur Q
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Cited by in corpus (6)

• Homotopy categories and idempotent completeness, weight structures and weight complex functors
• Baric structures on triangulated categories and coherent sheaves
• Staggered t-structures on derived categories of equivariant coherent sheaves
• A note on compactly generated co-t-structures
• On the quasi-hereditary property for staggered sheaves
• Introduction to staggered sheaves