Heights of Heegner cycles and derivatives of L-series
The author extends Gross and Zagier's limit formula to high weight modular forms by using arithmetic intersection theory. More precisely, he defines the (global) height pairing between CM-cycles in certain Kuga-Sato varieties, and shows an identity between the height pairings of Heegner cycles and coefficients of certain cusp forms of high weights. He gives some applications to the generalized Birch and Swinnerton-Dyer conjecture of Beilinson and Bloch, and to the algebraicity conjecture of Gross and Zagier. He also shows that the index conjecture of Gillet-Soulé and Beilinson-Bloch, and the Generalized Riemann Hypothesis have a common consequence: the positivity of the derivatives of certain L-series.
scientific article; zbMATH DE number 1058848