Algebraically constructible chains

Hélène Pennaneac'h[1]

  • [1] Université de Rennes I, IRMAR, Campus de Beaulieu, 35042 Rennes Cedex (France)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 4, page 939-994
  • ISSN: 0373-0956

Abstract

top
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.

How to cite

top

Pennaneac'h, Hélène. "Algebraically constructible chains." Annales de l’institut Fourier 51.4 (2001): 939-994. <http://eudml.org/doc/115941>.

@article{Pennaneach2001,
abstract = {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.},
affiliation = {Université de Rennes I, IRMAR, Campus de Beaulieu, 35042 Rennes Cedex (France)},
author = {Pennaneac'h, Hélène},
journal = {Annales de l’institut Fourier},
keywords = {algebraically constructible; homology; characteristic cycle; Nash manifold; Barel-Moore homology; algebraically constructible homology; real algebraic variety; constructible cycles; algebraically constructible functions},
language = {eng},
number = {4},
pages = {939-994},
publisher = {Association des Annales de l'Institut Fourier},
title = {Algebraically constructible chains},
url = {http://eudml.org/doc/115941},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Pennaneac'h, Hélène
TI - Algebraically constructible chains
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 4
SP - 939
EP - 994
AB - 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.
LA - eng
KW - algebraically constructible; homology; characteristic cycle; Nash manifold; Barel-Moore homology; algebraically constructible homology; real algebraic variety; constructible cycles; algebraically constructible functions
UR - http://eudml.org/doc/115941
ER -

References

top
  1. I. Bonnard, Un critère pour reconnaître les fonctions algébriquement constructibles, J. reine angew. Math. 526 (2000), 61-88 Zbl0959.14035MR1778301
  2. E. Becker, L. Bröcker, On the description of the reduced Witt ring, J. Alg. 52 (1978), 328-346 Zbl0396.10012MR506029
  3. J. Bochnak, M. Coste, M.-F. Roy, Géométrie algébrique réelle, Vol. 12 (1987), Springer Zbl0633.14016MR949442
  4. M.A. Dickmann, F. Miraglia, On quadratic forms whose total signature is zero mod 2 n , Invent. Math. 133 (1998), 243-278 Zbl0908.11022MR1632786
  5. C.G. Gibson, K. Wirthmüller, A.A. du Plessis, E. Looijenga, Topological stability of smooth mappings, Vol. 552 (1976), Springer-Verlag, Berlin-New York Zbl0377.58006MR436203
  6. R. Hartshorne, Algebraic Geometry, (1977), Springer Verlag Zbl0367.14001MR463157
  7. E. Kunz, Kähler Differentials, (1986), Friedr. Vieweg and Sohn, Braunschweig Zbl0587.13014MR864975
  8. M. Kashiwara, P. Schapira, Sheaves on manifolds, (1990), Springer-Verlag, Berlin Zbl0709.18001MR1074006
  9. M. Knebusch, C. Scheiderer, Einführung in die reelle Algebra, 63 (1989), Vieweg und Sohn, Braunschweig Zbl0732.12001MR1029278
  10. C. McCrory, A. Parusiński, Algebraically constructible functions, Ann. Scient. École Norm. Sup. (4) 30 (1997), 527-552 Zbl0913.14018MR1456244
  11. M. Rost, Chow groups with coefficients, Docu. Math. 1 (1996), 319-383 Zbl0864.14002MR1418952
  12. C. Scheiderer, Purity theorems for real spectra and applications, Real analytic and algebraic geometry (Trento, 1992) (1995), 229-250, of Gruyter, Berlin Zbl0840.14035
  13. W. Schmid, K. Vilonen, Characteristic cycles of constructible sheaves, Invent. Math. 124 (1996), 451-502 Zbl0851.32011MR1369425
  14. M. Schmid, Wittringhomologie 
  15. O. Zariski, P. Samuel, Commutative Algebra, (1958), van Nostrand, Princeton-London-Toronto Zbl0081.26501MR90581

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.