Homological periods and higher cycles
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912293302829056 |
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| author | Barbieri-Viale, L. |
| author_facet | Barbieri-Viale, L. |
| contents | For any scheme which is algebraic over a subfield of the complex numbers we here construct an homological regulator from Suslin homology to period homology and a higher cycle class map from Bloch's higher Chow group to the period Borel-Moore homology. Over algebraic numbers, making use of the motivic Albanese, we provide a purely geometric description of these period homologies in degree 1 and we characterise the $\mathbb{Q}/\mathbb{Z}$-cokernel of these regulators in terms of torsion zero-cycles, showing that Grothendieck period conjectures imply generalised Ro\uıtman theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19751 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homological periods and higher cycles Barbieri-Viale, L. Algebraic Geometry K-Theory and Homology Number Theory 14F42, 14F40, 14C30, 14L15 For any scheme which is algebraic over a subfield of the complex numbers we here construct an homological regulator from Suslin homology to period homology and a higher cycle class map from Bloch's higher Chow group to the period Borel-Moore homology. Over algebraic numbers, making use of the motivic Albanese, we provide a purely geometric description of these period homologies in degree 1 and we characterise the $\mathbb{Q}/\mathbb{Z}$-cokernel of these regulators in terms of torsion zero-cycles, showing that Grothendieck period conjectures imply generalised Ro\uıtman theorems. |
| title | Homological periods and higher cycles |
| topic | Algebraic Geometry K-Theory and Homology Number Theory 14F42, 14F40, 14C30, 14L15 |
| url | https://arxiv.org/abs/2503.19751 |