Purity and decomposition theorems for staggered sheaves

Details Purity and decomposition theorems for staggered sheaves Purity and decomposition theorems for staggered sheaves

2008-08-23

arxiv.org/abs/0808.3210v1

Mathematics

Algebraic Geometry

37 pages

Scientific paper

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.

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