法布尔--潘达里潘德循环消失的志村曲线

arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-13 DOI:arxiv-2409.08989

Congling Qiu

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摘要

格林（Green）和格里菲斯（Griffiths）的一个结果表明，对于属$g \geq 4$、有典型除数$K$的一般曲线$C$，其在$C/times C$上的法布尔--潘达里潘德0循环$K/times K-(2g-2)K_\Delta$ 在有理等价类的周群中是非扭转的。然而，对于Shimura曲线，我们证明它们的Faber--Pandharipande--0循环在理性上等价于0。

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Faber--Pandharipande Cycles vanish for Shimura curves

A result of Green and Griffiths states that for the generic curve $C$ of genus $g \geq 4$ with the canonical divisor $K$, its Faber--Pandharipande 0-cycle $K\times K-(2g-2)K_\Delta$ on $C\times C$ is nontorsion in the Chow group of rational equivalence classes. For Shimura curves, however, we show that their Faber--Pandharipande 0-cycles are rationally equivalent to 0. This is predicted by a conjecture of Beilinson and Bloch.

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arXiv - MATH - Algebraic Geometry

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