论文信息 - Height pairings for algebraic cycles on the product of a curve and a surface

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

For the productX = C×S of a curve and a surface over a number field, we construct unconditionally a Beilinson–Bloch type height pairing ([1, 2]) for homologically trivial algebraic cycles on X. Then for an embedding f : C−→S, we define an arithmetic diagonal cycle modified from the graph of f . This work extends previous work of Gross and Schoen [7] when S is the product of two curves, and is based on our recent work [14] which relates the height pairings and the standard conjectures.

Shou-Wu Zhang

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