Height pairings for algebraic cycles on the product of a curve and a surface
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916418225700864 |
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| author | Zhang, Shou-Wu |
| author_facet | Zhang, Shou-Wu |
| contents | For the product $X=C\times S$ of a curve and a surface over a number field, we construct unconditionally a Beilinson--Bloch type height pairing for homologically trivial algebraic cycles on $X$. Then for an embedding $f: C\to S$, we define an arithmetic diagonal cycle modified from the graph of $f$. This work extends previous work of Gross and Schoen when $S$ is the product of two curves, and is based on our recent work which relates the height pairings and the standard conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_10276 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Height pairings for algebraic cycles on the product of a curve and a surface Zhang, Shou-Wu Algebraic Geometry Number Theory For the product $X=C\times S$ of a curve and a surface over a number field, we construct unconditionally a Beilinson--Bloch type height pairing for homologically trivial algebraic cycles on $X$. Then for an embedding $f: C\to S$, we define an arithmetic diagonal cycle modified from the graph of $f$. This work extends previous work of Gross and Schoen when $S$ is the product of two curves, and is based on our recent work which relates the height pairings and the standard conjectures. |
| title | Height pairings for algebraic cycles on the product of a curve and a surface |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2111.10276 |