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The affine stratification number and the moduli space of curves
[chapter]

2004
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CRM Proceedings and Lecture notes AMS
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We define the affine stratification number asn X of a scheme X. For X equidimensional, it is the minimal number k such that there is a stratification of X by locally closed affine subschemes of codimension at most k. We show that the affine stratification number is well-behaved, and bounds many aspects of the topological complexity of the scheme, such as vanishing of cohomology groups of quasicoherent, constructible, and -adic sheaves. We explain how to bound asn X in practice. We give a series

doi:10.1090/crmp/038/10
fatcat:kyyvjobpajggxm2wtae75zw3re