A Gersten complex on real schemes
Fangzhou Jin, Heng Xie
TL;DR
This paper explores a Gersten complex on real schemes, linking duality theories and providing a dualizing object that connects algebraic and topological invariants, with implications for Borel-Moore homology.
Contribution
It introduces a Gersten-type complex that bridges coherent and Verdier duality on real schemes, establishing a dualizing object compatible with the inverse image functor.
Findings
Hypercohomology matches that of the Gersten-Witt complex.
The complex relates to topological and semialgebraic Borel-Moore homology in some cases.
Provides a new duality framework for 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 . 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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models