On the real cycle class map for singular varieties
Abstract We investigate the real cycle class map for singular varieties. We introduce an analog of Borel–Moore homology for algebraic varieties over the real numbers, which is defined via the hypercohomology of the Gersten–Witt complex associated with schemes possessing a dualizing complex. We show that the hypercohomology of this complex is isomorphic to the classical Borel–Moore homology for quasi-projective varieties over the real numbers.
Authors
- Fangzhou Jin
- Heng Xie (ORCID: https://orcid.org/0000-0001-9516-8444)
Institutions
- Tongji University (CN)
- Sun Yat-sen University (CN)
Publication Details
- Journal
- Journal of Homotopy and Related Structures
- Published
- 2025-04-21
- DOI
- https://doi.org/10.1007/s40062-025-00369-6
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- European Commission
- Deutsche Forschungsgemeinschaft
- National Natural Science Foundation of China
- Sun Yat-sen University
- Engineering and Physical Sciences Research Council
- National Key Research and Development Program of China
- Fundamental Research Funds for the Central Universities