Here we prove a Poincaré - Verdier duality theorem for the o-minimal sheaf cohomology with definably compact supports of definably normal, definably locally compact spaces in an arbitrary o-minimal structure.
On démontre une dualité de Poincaré - Verdier dans le cadre de la cohomologie o-minimale des faisceaux avec support compact et définissable sur des espaces définissablement normaux, définissablement localement compacts dans une structure o-minimale arbitraire.
Keywords: O-minimal structures, sheaf cohomology
Mot clés : Structure o-minimale, cohomologie des faisceaux
Edmundo, Mário J. 1; Prelli, Luca 2
@article{AIF_2010__60_4_1259_0, author = {Edmundo, M\'ario J. and Prelli, Luca}, title = {Poincar\'e - {Verdier} duality in o-minimal structures}, journal = {Annales de l'Institut Fourier}, pages = {1259--1288}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {4}, year = {2010}, doi = {10.5802/aif.2554}, mrnumber = {2722241}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2554/} }
TY - JOUR AU - Edmundo, Mário J. AU - Prelli, Luca TI - Poincaré - Verdier duality in o-minimal structures JO - Annales de l'Institut Fourier PY - 2010 SP - 1259 EP - 1288 VL - 60 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2554/ DO - 10.5802/aif.2554 LA - en ID - AIF_2010__60_4_1259_0 ER -
%0 Journal Article %A Edmundo, Mário J. %A Prelli, Luca %T Poincaré - Verdier duality in o-minimal structures %J Annales de l'Institut Fourier %D 2010 %P 1259-1288 %V 60 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2554/ %R 10.5802/aif.2554 %G en %F AIF_2010__60_4_1259_0
Edmundo, Mário J.; Prelli, Luca. Poincaré - Verdier duality in o-minimal structures. Annales de l'Institut Fourier, Volume 60 (2010) no. 4, pp. 1259-1288. doi : 10.5802/aif.2554. https://aif.centre-mersenne.org/articles/10.5802/aif.2554/
[1] Corrigendum to “Transfer methods for o-minimal topology”, J. Symb. Logic, Volume 72 (2007) no. 3, pp. 1079-1080 | DOI | MR | Zbl
[2] Transfer methods for o-minimal topology, J. Symb. Logic, Volume 68 (2003) no. 3, pp. 785-794 | DOI | MR | Zbl
[3] Real Algebraic Geometry, Springer-Verlag, 1998 | MR | Zbl
[4] Sheaf theory, Second Edition, Springer-Verlag, 1997 | MR | Zbl
[5] An introduction to o-minimal geometry, Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Istituti Editoriali e Poligrafici Internazionali, Pisa (2000). Available in RAAG preprint server (http://ihp-raag.org/) | MR
[6] La topologie du spectre réel, in Ordered fields and real algebraic geometry, Contemporary Mathematics, Volume 8 (1982), pp. 27-59 | MR | Zbl
[7] The homotopy axiom in semi-algebraic sheaf cohomology, J. reine angew. Maths., Volume 355 (1985), pp. 108-128 | DOI | MR | Zbl
[8] Homology of locally semialgebraic spaces, LNM 1484, Springer-Verlag, 1991 | MR | Zbl
[9] On the homology of algebraic varieties over real closed fields, J. reine u.angew. Math., Volume 335 (1982), pp. 122-163 | DOI | MR | Zbl
[10] Lectures on algebraic topology, Springer-Verlag, 1995 | MR | Zbl
[11] Covering definable manifolds by open definable subsets, In: Logic Colloquium ’05, 28, Lecture Notes in Logic, 2008 (ed., C. Dimitracopoulos et al.) Cambridge University Press | MR | Zbl
[12] Sheaf cohomology in o-minimal structures, J. Math. Logic, Volume 6 (2006) no. 2, pp. 163-179 | DOI | MR | Zbl
[13] Definably compact abelian groups, J. Math. Log., Volume 4 (2004) no. 2, pp. 163-180 | DOI | MR | Zbl
[14] Comparation theorems for o-minimal singular (co)homology, Trans. Amer. Math. Soc., Volume 360 (2008) no. 9, pp. 4889-4912 | DOI | MR | Zbl
[15] The Lefschetz coincidence theorem in o-minimal expansions of fields, Topology Appl., Volume 156 (2009) no. 15, pp. 2470-2484 | DOI | MR | Zbl
[16] Théorie des faisceaux, Hermann, 1958 | MR
[17] Cohomology of sheaves, Springer Verlag, 1986 | MR
[18] Sheaves on manifolds, Springer Verlag, 1990 | MR | Zbl
[19] Ind-sheaves, 271, Astérisque, 2001 (136 pp) | MR | Zbl
[20] Categories and sheaves, Springer Verlag, 2005 | MR | Zbl
[21] Sheaves of continuous definable functions, J. Symb. Logic, Volume 53 (1988) no. 4, pp. 1165-1169 | DOI | MR | Zbl
[22] Sheaves on subanalytic sites, Rend. Sem. Mat. Univ. Padova, Volume 120 (2008), pp. 167-216 | Numdam | MR | Zbl
[23] Tame topology and o-minimal structures, Cambridge University Press, 1998 | MR | Zbl
[24] Covering definable open subsets by open cells, In: O-minimal Structures, Proceedings of the RAAG Summer School Lisbon 2003, Lecture Notes in Real Algebraic and Analytic Geometry (M. Edmundo, D. Richardson and A. Wilkie eds.), Cuvillier Verlag, 2005
[25] O-minimal homology, PhD. Thesis (1996), University of Illinois at Urbana-Champaign
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