Complexe de poids des variétés algébriques réelles avec action

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.

in French

References in corpus (2)

• Motivic Igusa zeta functions
• Topology of singular algebraic varieties

Cited by in corpus (1)

• Equivariant weight filtration for real algebraic varieties with action