Mathematics > Algebraic Geometry
[Submitted on 19 Nov 2021 (v1), last revised 30 Apr 2024 (this version, v4)]
Title:Height pairings for algebraic cycles on the product of a curve and a surface
View PDF HTML (experimental)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.
Submission history
From: Shou-Wu Zhang [view email][v1] Fri, 19 Nov 2021 15:25:44 UTC (14 KB)
[v2] Wed, 1 Dec 2021 03:16:47 UTC (17 KB)
[v3] Mon, 8 May 2023 18:32:48 UTC (17 KB)
[v4] Tue, 30 Apr 2024 19:20:05 UTC (18 KB)
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