Algebraically constructible chains

Pennaneac'h, Hélène

doi:10.5802/aif.1841

Algebraically constructible chains
[Chaî nes algébriquement constructibles]

Pennaneac'h, Hélène ¹

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.

Résumé
Abstract

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.

MR Zbl

DOI : 10.5802/aif.1841

Classification : 14P25, 14F43
Keywords: algebraically constructible, homology, characteristic cycle
Mot clés : algébriquement constructible, homologie, cycle caractéristique

Affiliations des auteurs :

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},
     journal = {Annales de l'Institut Fourier},
     pages = {939--994},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {51},
     number = {4},
     year = {2001},
     doi = {10.5802/aif.1841},
     mrnumber = {1849211},
     zbl = {1036.14029},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1841/}
}

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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. http://www.numdam.org/articles/10.5802/aif.1841/

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