On the integral Hodge conjecture for real varieties, I

• 成果类型: Article
• 署名作者: Benoist, Olivier; Wittenberg, Olivier
• 署名单位: Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00965-8
• 发表日期: 2020
• 页码: 1-77
• 关键词: semi-algebraic topology; homology classes; closed field; cycles; COHOMOLOGY; THEOREMS; CURVES; submanifolds; EQUIVALENCE; torsion

摘要

We formulate the real integral Hodge conjecture, a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi-Yau threefolds and on rationally connected varieties. We relate it to the problem of determining the image of the Borel-Haefliger cycle class map for 1-cycles, with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the Chow group of 1-cycles of real threefolds. New results about these problems are obtained along the way.