In this talk, we consider a conjecture by Gross and Kudla that relates the derivatives of triple-product L-functions  for three modular forms and the height pairing of the Gross—Schoen cycles on Shimura curves.

Then, we sketch a proof of a generalization of this conjecture for Hilbert modular forms in the spherical case. This is a report of work in progress with Xinyi Yuan and Wei Zhang, with help from Yifeng Liu.