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Diagonal cycles and triple L-series

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For a smooth and projective curve, Gross and Schoen have constructed a (modified and cohomologically trivial) diagonal cycle. In modular curve case, Gross and Kulda have conjectured that the heights of the Hecke components of this cycle are related to the derivatives of triple L-series of modular forms. In this talk, I will outline a proof of the conjecture, and explain some consequences in Beilinson-Bloch conjecture and Bogomolov conjecture.

This talk is part of the Kuwait Foundation Lectures series.

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