Constructible functions on Artin stacks
| dc.creator | Joyce, Dominic | |
| dc.date | 2004-03-18 | |
| dc.date | 2006-01-04 | |
| dc.date.accessioned | 2026-07-07T07:41:55Z | |
| dc.date.available | 2026-07-07T07:41:55Z | |
| dc.description | 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 in X(K) is a finite union of subsets Y(K) for finite type subschemes Y in X. A constructible function f : X(K) --> Q has f(X(K)) finite and f^{-1}(c) constructible for all nonzero c. Write CF(X) for the Q-vector space of constructible functions on X. Let phi : X --> Y and psi : Y --> Z be morphisms of C-varieties. MacPherson defined a Q-linear "pushforward" CF(phi) : CF(X) --> CF(Y) by "integration" w.r.t. the topological Euler characteristic. It is functorial, that is, CF(psi o phi)=CF(psi) o CF(phi). This was extended to K of characteristic zero by Kennedy. This paper generalizes these results to K-schemes and Artin K-stacks with affine stabilizers. We define notions of Euler characteristic for constructible sets in K-schemes and K-stacks, and pushforwards and pullbacks of constructible functions, with functorial behaviour. Pushforwards and pullbacks commute in Cartesian squares. We also define "pseudomorphisms", a generalization of morphisms well suited to constructible functions problems. | |
| dc.description | 25 pages, LaTeX. (v7) shorter: material moved to math.AG/0509722 | |
| dc.identifier | https://arxiv.org/abs/math/0403305 | |
| dc.identifier | http://arxiv.org/abs/math/0403305 | |
| dc.identifier | Journal of the London Mathematical Society 74 (2006), 583-606. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122297 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Constructible functions on Artin stacks | |
| dc.type | text |