A higher Gross-Zagier type formula for moduli of shtukas at deeper level

We generalize the function field analogue analogue of the Gross-Zagier and Waldspurger formulae due to Yun and Zhang relating the (higher) derivative of an automorphic (base change) L-function to intersection numbers of Heegner-Drinfeld cycles on moduli spaces of shtukas to not necessarily square-free level.

The main new input is the study of the geometry and cohomology of the appropriate ``integral models'' of moduli spaces of shtukas at deeper level.