  We discuss a connection between coherent duality and Verdier duality via a
Gersten-type complex of sheaves on real schemes, and show that this
construction gives a dualizing object in the derived category, which is
compatible with the exceptional inverse image functor $f^!$. The
hypercohomology of this complex coincides with hypercohomology of the
sheafified Gersten-Witt complex, which in some cases can be related to
topological or semialgebraic Borel-Moore homology.
