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On the real cycle class map for singular varieties

Year: 2025
Type: article
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.
DOI: 10.1007/s40062-025-00369-6
Language: English
Open Access status: hybrid
Estimated APC paid: $3,290
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
Awards: G1985268728, G310134133, G434337789, Higher Grothendieck-Witt groups and A1-homotopy theory, G5159938104, G6665767358, G6754795756, G8438232881
OpenAlex ID: W4409640290
FWCI:
Cites: 28
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Related to: 10