Jacob Tsimerman - Large Compact Subvarieties of A_g
Visions in Arithmetic and Beyond: Celebrating Peter Sarnak's Work and Impact
June 7, 2024
(Joint with Samuel Grushevsky, Gabriele Mondello, Riccardo Salvati Manni) We determine the maximal dimension of a compact subvariety of the moduli space of principally polarized abelian varieties Ag for any value of g. For g g16 the dimension is g−1, while for g16, it is determined by the larged dimensional compact Shimura subvariety, which we determine. Our methods rely on deforming the boundary using special varieties, and functional transcendence theory.