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arXiv · 2007.04625

A Gersten complex on real schemes

Fangzhou Jin·Heng Xie
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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.

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Fangzhou Jin, Heng Xie. 2020-07-09. A Gersten complex on real schemes. https://doi.org/10.1007/s40062-025-00369-6

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