A Gersten complex on real schemes

Abstract

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.