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arXiv · 2111.10276

Height pairings for algebraic cycles on the product of a curve and a surface

Shou-Wu Zhang
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Abstract

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.

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Shou-Wu Zhang. 2021-11-19. Height pairings for algebraic cycles on the product of a curve and a surface. https://doi.org/10.2140/tunis.2024.6.481

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