Algebraic Geometry Seminar
For a very general complex abelian variety X of dimension 3, the mod p Chow group of 1-cycles on X is infinite for every prime number p. In particular, these are the first known examples of complex varieties with infinite Chow groups modulo 2. This result shows the complexity of curves on a 3-fold, compared to the simplicity of codimension-1 sub varieties. I will explain the background, including related examples by Griffiths, Schoen, Nori, Rosenschon, and Srinivas. The proof uses some p-adic Hodge theory as well as a geometric construction of "interesting" curves on the 3-fold.