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Algebraically constructible chains. (English) Zbl 1036.14029
Summary: 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.
Reviewer: Reviewer (Berlin)

##### MSC:
 14P25 Topology of real algebraic varieties 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 14P20 Nash functions and manifolds
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