Abstract: 

The Gross–Zagier formula relates the Néron–Tate heights of Heegner points on elliptic curves to the central derivative of the associated L-functions. A function field analogue was established by Yun–Zhang, relating the self-intersection numbers of special cycles on PGL_2-Shtukas to higher central derivatives of standard base change L-functions.

In this talk, I will present a higher-dimensional analogue of this formula over function fields, relating the self-intersection numbers of diagonal cycles on G-Shtukas to certain higher non-central derivatives of adjoint L-functions. Compared with previous works, we allow arbitrary semisimple groups and arbitrary modification types. This work is motivated by ongoing work of Chen–Lu–Zhang.