Course MAT517

Topics in Arithmetic Geometry: Arithmetic Gan-Gross-Prasad Conjecture

I will start with geometry and arithmetic of abelian varieties, including the moduli spaces, Mordell-Weil theorem, the Birch and Swinnerton-Dyer conjecture, and their conjectured  high codimension analogues by Beilinson and Bloch.  Then, I will introduce Gross-Zagier type formulae for Shimura curves and their triple products, high codimensional analogues by Gan-Gross-Prasad for unitary Shimura varieties, and  a relative trace formula approach by Wei Zhang.