Constructible Functions on Artin Stacks

@inproceedings{JoyceConstructibleFO,
  title={Constructible Functions on Artin Stacks},
  author={Dominic Joyce and Lincoln College and Oxford and Tom Bridgeland and Frances Kirwan and Andrew Kresch and J. Sch{\"u}rmann and Bertrand Toen and Burt Totaro}
}
Let K be an algebraically closed field, X a K-scheme, and X(K) the set of closed points in X. A constructible set C ⊆ X(K) is a finite union of subsets Y (K) for finite type K-subschemes Y in X. A constructible function f : X(K) → Q has f (X(K)) finite and f −1 (c) constructible for all 0 = c ∈ f (X(K)). Write CF(X) for the Q-vector space of constructible functions on X. Let φ : X → Y and ψ : Y → Z be morphisms of C-varieties. MacPherson [16, Prop. 1] defined a Q-linear pushforward CF(φ) : CF(X… CONTINUE READING
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