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Benedict H. Gross; Chad Schoen
The modified diagonal cycle on the triple product of a pointed curve
Annales de l'institut Fourier, 45 no. 3 (1995), p. 649-679, doi: 10.5802/aif.1469
Article PDF | Reviews MR 96e:14008 | Zbl 0822.14015 | 1 citation in Cedram

Résumé - Abstract

Let $X$ be a curve over a field $k$ with a rational point $e$. We define a canonical cycle $\Delta _e\in Z^2(X^3)_{{\rm hom}}$. Suppose that $k$ is a number field and that $X$ has semi-stable reduction over the integers of $k$ with fiber components non-singular. We construct a regular model of $X^3$ and show that the height pairing $\langle \tau _*(\Delta _e),\tau ^{\prime }_*(\Delta _e)\rangle $ is well defined where $\tau $ and $\tau ^{\prime }$ are correspondences. The paper ends with a brief discussion of heights and $L$-functions in the case that $X$ is a modular curve.

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