Shtukas and the Taylor expansion of L-functions

We define the Heegner Drinfeld cycle on the moduli stack of Drinfeld Shtukas of rank two with r-modifications for an even integer r. We prove an identity between (1) the r-th central derivative of the quadratic base change L-function associated to an everywhere unramified cuspidal automorphic representation pi of PGL(2), and (2) the self-intersection number of the pi-isotypic component of the Heegner Drinfeld cycle. This identity can be viewed as a function-field analog of the Waldspurger and Gross-Zagier formula for higher derivatives of L-functions.