Speaker
Arnaud Beauville
Abstract
Let C be a curve of genus >2, embedded in its Jacobian JC. The cycle [C]-[(-1)*C] is cohomologous to zero in JC; is it algebraically equivalent to zero? The answer is negative for C general (Ceresa, 1983) and for some very particular curves, and positive (trivially) for hyperelliptic curves. I will explain an example, obtained with C. Schoen, of a non-hyperelliptic curve C for which [C]-[(-1)^*C] is torsion modulo algebraic equivalence.