Heights of CM cycles and derivatives of L-series

Yara Elias; Tian An Wong

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arXiv · 1708.05820

Heights of CM cycles and derivatives of L-series

Yara Elias·Tian An Wong

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Abstract

We extend the work of S. Zhang and Yuan-Zhang-Zhang to obtain a Gross-Zagier formula for modular forms of even weight in terms of an arithmetic intersection pairing of CM-cycles on Kuga-Sato varieties over Shimura curves. Combined with a result of the first author and de Vera-Piquero adapting Kolyvagin's method of Euler systems to this setting, we bound the associated Selmer and Tate-Shafarevich groups, assuming the non-vanishing of the derivative of the L-function at the central point.

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Yara Elias, Tian An Wong. 2017-08-19. Heights of CM cycles and derivatives of L-series. https://arxiv.org/abs/1708.05820

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