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arXiv · 1211.4152

Complexe de poids des variétés algébriques réelles avec action

Fabien Priziac
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Abstract

Using the functoriality of C. McCrory and A. Parusiński's weight complex -which induces an analog of the weight filtration for complex algebraic varieties on the Borel-Moore homology with $\mathbb{Z}_2$ coefficients of real algebraic varieties-, we define a weight complex with action on the real algebraic varieties equipped with a finite group action. Emphasizing on the two elements group, we then establish a filtered version of Smith short sequence, taking into account the Nash-constructible filtration which realizes the weight complex with action. Its exactness is implied by the splitting of a Nash manifold equipped with an algebraic involution along an arc-symmetric subset.

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Fabien Priziac. 2013-12-12. Complexe de poids des variétés algébriques réelles avec action. https://doi.org/10.1007/s00209-013-1244-8

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