**V. Srinivas**

TIFR

November 18, 2010

**Cycles on a generic complex abelian 3-fold**:
The Chow groups $CH^i(X)$ of a complex projective manifold $X$ have a
rather complicated structure, in general, but one might hope that for a prime $p$, the $p$-torsion and $p$-cotorsion subgroups are more easy to understand.
I will first survey the ``classical'' finiteness results for the
$p$-torsion and $p$-cotorsion, and then discuss examples, based on joint work with A. Rosenschon, to show that outside this classical realm, the $p$-torsion and $p$-cotorsion are in general infinite. Our work builds on earlier works of Ceresa, Nori, Bloch-Esnault and Schoen, which I will also discuss briefly.