Constructible Functions on Artin Stacks

By D. Joyce. 2004

59 citations recorded by the source corpus.

Let 핂 be an algebraically closed field, let X be a 핂‐variety, and let X(핂) be the set of closed points in X. A constructible set C in X(핂) is a finite union of subsets Y(핂) for subvarieties Y in X. A constructible function f : X(핂) → ℚ has f(X(핂)) finite and f−1(c) constructible for all c ≠ 0. Write CF(X) for the vector space of such f. Let φ : X → Y and ψ : Y → Z be morphisms of ℂ‐varieties. MacPherson defined a linear pushforward CF(φ) : CF(X) → CF(Y) by ‘integration’ with respect to the topological Euler characteristic. It is functorial, that is, CF(ψ ○ φ) = CF(ψ) ○ CF(φ). This was extended to 핂 of characteristic zero by Kennedy.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/be66556a7edf4353e1cdf75e7925b4f31458c365

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Citations in the corpus

A theory of generalized Donaldson–Thomas invariants (2008, methodology): “11) are integrals of constructible functions using Euler characteristic as measure, as in [49].”
An introduction to motivic Hall algebras (2010, background): “For definitions of constructible functions on stacks see [8].”
MOTIVIC INVARIANTS OF ARTIN STACKS AND ‘STACK FUNCTIONS’ (2005, methodology): “ a 1-isomorphism E∼= F×H G. Cartesian squares may also be characterized by a universal property. 2.3 Constructible functions onstacks Finally we discuss constructible functions on K-stacks, following [8]. For this section we need Kto have characteristic zero. Deﬁnition 2.4. Let Fbe an algebraic K-st”
Buildings, spiders, and geometric Satake (2011, background): “If X is a proper complex algebraic variety over C and f : X → C is a constructible function, then we define the Euler characteristic integral (see [31] or [17]) ∫”