no. 4
Algebraically constructible chains
[Chaî nes algébriquement constructibles]
Pennaneac'h, Hélène1
1 Université de Rennes I, IRMAR, Campus de Beaulieu, 35042 Rennes Cedex (France)
Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 939-994.

On construit pour une variété algébrique réelle (plus généralement, pour un schéma essentiellement de type fini sur un corps de caractéristique 0) des complexes de chaînes algébriquement constructibles et k-algébriquement constructibles, dont on étudie la fonctorialité et dont on calcule l’homologie pour les espaces affines et projectifs. Puis on montre que les cycles lagrangiens algébriquement constructibles du fibré cotangent sont exactement les cycles caractéristiques des fonctions algébriquement constructibles.

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.

DOI : 10.5802/aif.1841
Classification : 14P25, 14F43
Keywords: algebraically constructible, homology, characteristic cycle
Mot clés : algébriquement constructible, homologie, cycle caractéristique

Pennaneac'h, Hélène 1

1 Université de Rennes I, IRMAR, Campus de Beaulieu, 35042 Rennes Cedex (France) 
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     title = {Algebraically constructible chains},
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Pennaneac'h, Hélène. Algebraically constructible chains. Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 939-994. doi : 10.5802/aif.1841. https://aif.centre-mersenne.org/articles/10.5802/aif.1841/

[B] I. Bonnard Un critère pour reconnaître les fonctions algébriquement constructibles, J. reine angew. Math., Volume 526 (2000), pp. 61-88 | DOI | MR | Zbl

[BB] E. Becker; L. Bröcker On the description of the reduced Witt ring, J. Alg., Volume 52 (1978), pp. 328-346 | DOI | MR | Zbl

[BCR] J. Bochnak; M. Coste; M.-F. Roy Géométrie algébrique réelle, Ergebnisse der Math., 3 Folge, Vol. 12, Springer, 1987 | MR | Zbl

[DM] M.A. Dickmann; F. Miraglia On quadratic forms whose total signature is zero mod 2 n , Invent. Math., Volume 133 (1998) no. 2, pp. 243-278 | DOI | MR | Zbl

[G] C.G. Gibson; K. Wirthmüller; A.A. du Plessis; E. Looijenga Topological stability of smooth mappings, Lecture Notes in Mathematics, Vol. 552, Springer-Verlag, Berlin-New York, 1976 | MR | Zbl

[Ha] R. Hartshorne Algebraic Geometry, Graduate Texts in Math., Springer Verlag, 1977 | MR | Zbl

[KnS] M. Knebusch; C. Scheiderer Einführung in die reelle Algebra, Vieweg Studium: Aufbaukurs Mathematik, 63, Vieweg und Sohn, Braunschweig, 1989 | MR | Zbl

[KS] M. Kashiwara; P. Schapira Sheaves on manifolds, Springer-Verlag, Berlin, 1990 | MR | Zbl

[Ku] E. Kunz Kähler Differentials, Advanced Lectures in Math., Friedr. Vieweg and Sohn, Braunschweig, 1986 | MR | Zbl

[MP] C. McCrory; A. Parusiński Algebraically constructible functions, Ann. Scient. École Norm. Sup. (4), Volume 30 (1997), pp. 527-552 | Numdam | MR | Zbl

[R] M. Rost Chow groups with coefficients, Docu. Math., Volume 1 (1996), pp. 319-383 | MR | Zbl

[S] M. Schmid Wittringhomologie Thesis University of Regensburg (available on the web page of M. Rost), http://www.math.ohio-state.edu/~rost/papers.html

[Sch] C. Scheiderer Purity theorems for real spectra and applications, Real analytic and algebraic geometry (Trento, 1992) (1995), pp. 229-250 | Zbl

[SV] W. Schmid; K. Vilonen Characteristic cycles of constructible sheaves, Invent. Math., Volume 124 (1996), pp. 451-502 | DOI | MR | Zbl

[ZS] O. Zariski; P. Samuel Commutative Algebra, van Nostrand, Princeton-London-Toronto, 1958 | MR | Zbl

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