In this paper we find general criteria for invariance and finiteness results for -minimal cohomology in an arbitrary -minimal structure. We apply our criteria and obtain new invariance and finiteness results for -minimal cohomology in -minimal expansions of ordered groups and for the -minimal cohomology of definably compact definable groups in arbitrary -minimal structures.
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Mots clés : $o$-minimal structures, $o$-minimal cohomology.
@article{CML_2015__7_1_35_0,
author = {Edmundo, M\'ario J. and Prelli, Luca},
title = {Invariance of $o$-minimal cohomology with definably compact supports},
journal = {Confluentes Mathematici},
pages = {35--53},
publisher = {Institut Camille Jordan},
volume = {7},
number = {1},
year = {2015},
doi = {10.5802/cml.17},
language = {en},
url = {http://www.numdam.org/articles/10.5802/cml.17/}
}
TY - JOUR AU - Edmundo, Mário J. AU - Prelli, Luca TI - Invariance of $o$-minimal cohomology with definably compact supports JO - Confluentes Mathematici PY - 2015 SP - 35 EP - 53 VL - 7 IS - 1 PB - Institut Camille Jordan UR - http://www.numdam.org/articles/10.5802/cml.17/ DO - 10.5802/cml.17 LA - en ID - CML_2015__7_1_35_0 ER -
%0 Journal Article %A Edmundo, Mário J. %A Prelli, Luca %T Invariance of $o$-minimal cohomology with definably compact supports %J Confluentes Mathematici %D 2015 %P 35-53 %V 7 %N 1 %I Institut Camille Jordan %U http://www.numdam.org/articles/10.5802/cml.17/ %R 10.5802/cml.17 %G en %F CML_2015__7_1_35_0
Edmundo, Mário J.; Prelli, Luca. Invariance of $o$-minimal cohomology with definably compact supports. Confluentes Mathematici, Tome 7 (2015) no. 1, pp. 35-53. doi : 10.5802/cml.17. http://www.numdam.org/articles/10.5802/cml.17/
[1] A. Berarducci and A. Fornasiero O-minimal cohomology: finiteness and invariance results J. Math. Logic 9 (2) (2009) 167–182.
[2] A. Berarducci and M. Otero O-minimal fundamental group, homology and manifolds J. London Math. Soc. 65 (2) (2002) 257–270.
[3] J. Bochnak, M. Coste and M-F. Roy Real algebraic geometry Springer-Verlag 1998.
[4] G. Bredon Sheaf theory Second Edition Springer-Verlag 1997.
[5] M. Coste An introduction to -minimal geometry Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Istituti Editoriali e Poligrafici Internazionali, Pisa (2000).
[6] M. Carral and M. Coste Normal spectral spaces and their dimensions J. Pure and Appl. Algebra 30 (3) (1983) 227–235.
[7] M. Coste and M.-F. Roy La topologie du spectre réel in Ordered fields and real algebraic geometry, Contemporary Mathematics 8 (1982) 27–59.
[8] H. Delfs Homology of locally semialgebraic spaces LNM 1484 Springer-Verlag 1991.
[9] L. van den Dries Tame topology and -minimal structures Cambridge University Press 1998.
[10] M. Edmundo, G. Jones and N. Peatfield Sheaf cohomology in -minimal structures J. Math. Logic 6 (2) (2006) 163–179.
[11] M. Edmundo, M. Mamino and L. Prelli On definably proper maps Fund. Math. (to appear).
[12] M. Edmundo and M. Otero Definably compact abelian groups J. Math. Logic 4 (2) (2004) 163–180.
[13] M. Edmundo and L. Prelli Poincaré - Verdier duality in -minimal structures Ann. Inst. Fourier Grenoble 60 (4) (2010) 1259–1288.
[14] M. Edmundo and L. Prelli Sheaves on T-topologies J. Math. Soc. Japan (to appear).
[15] M. Edmundo and G. Terzo A note on generic subsets of definable groups Fund. Math. 215 (1) (2011) 53–65.
[16] M. Edmundo and A. Woerheide Comparision theorems for -minimal singular (co)homology Trans. Amer. Math. Soc. 360 (9) (2008) 4889–4912.
[17] P. Eleftheriou A semi-linear group which is not affine Ann. Pure Appl. Logic 156 (2008) 287 – 289.
[18] P. Eleftheriou, Y. Peterzil and J. Ramakrishnan Interpretable groups are definable J. Math. Log. 14 1450002 (2014) [47 pages].
[19] A. Fornasiero O-minimal spectrum Unpublished, 33pp, 2006. http://www.dm.unipi.it/~fornasiero/articles/spectrum.pdf
[20] R. Godement Théorie des faisceaux Hermann 1958.
[21] B. Iversen Cohomology of sheaves Springer Verlag 1986.
[22] M. Kashiwara and P. Schapira Sheaves on manifolds Springer Verlag 1990.
[23] M. Otero A survey on groups definable in -minimal structures in Model Theory with Applications to Algebra and Analysis, vol. 2, Editors: Z. Chatzidakis, D. Macpherson, A. Pillay and A. Wilkie, LMS LNS 350 Cambridge Univ. Press (2008) 177–206
[24] Y. Peterzil and C. Steinhorn Definable compactness and definable subgroups of -minimal groups J. London Math. Soc. 59 (2) (1999) 769–786.
[25] A. Pillay On groups and fields definable in -minimal structures J. Pure Appl. Algebra 53 (1988) 239 – 255.
[26] A. Pillay Sheaves of continuous definable functions J. Symb. Logic 53 (4) (1988) 1165–1169.
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