×

zbMATH — the first resource for mathematics

Algebraically constructible chains. (English) Zbl 1036.14029
Summary: We construct for a real algebraic variety (or more generally for a scheme essentially of finite type over a field of characteristic 0) complexes of algebraically and \(k\)-algebraically constructible chains. We study their functoriality and compute their homologies for affine and projective spaces. Then we show that the Lagrangian algebraically constructible cycles of the cotangent bundle are exactly the characteristic cycles of the algebraically constructible functions.
Reviewer: Reviewer (Berlin)

MSC:
14P25 Topology of real algebraic varieties
14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
14P20 Nash functions and manifolds
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[1] Un critère pour reconnaître LES fonctions algébriquement constructibles, J. reine angew. Math., 526, 61-88, (2000) · Zbl 0959.14035
[2] On the description of the reduced Witt ring, J. Alg., 52, 328-346, (1978) · Zbl 0396.10012
[3] Géométrie algébrique réelle, Vol. 12, (1987), Springer · Zbl 0633.14016
[4] On quadratic forms whose total signature is zero mod \(2^n,\) Invent. Math., 133, 2, 243-278, (1998) · Zbl 0908.11022
[5] Topological stability of smooth mappings, Vol. 552, (1976), Springer-Verlag, Berlin-New York · Zbl 0377.58006
[6] Algebraic Geometry, (1977), Springer Verlag · Zbl 0367.14001
[7] Einführung in die reelle Algebra, 63, (1989), Vieweg und Sohn, Braunschweig · Zbl 0732.12001
[8] Sheaves on manifolds, (1990), Springer-Verlag, Berlin · Zbl 0709.18001
[9] Kähler Differentials, (1986), Friedr. Vieweg and Sohn, Braunschweig · Zbl 0587.13014
[10] Algebraically constructible functions, Ann. Scient. École Norm. Sup. (4), 30, 527-552, (1997) · Zbl 0913.14018
[11] Chow groups with coefficients, Docu. Math., 1, 319-383, (1996) · Zbl 0864.14002
[12] Wittringhomologie
[13] Purity theorems for real spectra and applications, Real analytic and algebraic geometry (Trento, 1992), 229-250, (1995), of Gruyter, Berlin · Zbl 0840.14035
[14] Characteristic cycles of constructible sheaves, Invent. Math., 124, 451-502, (1996) · Zbl 0851.32011
[15] Commutative Algebra, (1958), van Nostrand, Princeton-London-Toronto · Zbl 0081.26501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.