Talk page
Title:
Two coniveau filtrations and algebraic equivalence over finite fields
Speaker:
Abstract:
Over the complex numbers, the integral cohomology of a smooth projective variety is endowed with the coniveau and strong coniveau filtrations. The two filtrations differ in general as recently shown by Benoist and Ottem, and this result may be exnteded to the l-adic setting over any algebraically closed field of characteristic not 2. In this talk, I would like to discuss some consequences of the equality of the two filtrations for algebraic equivalence for codimension 2 cycles over finite fields. As an application, we show the vanishing of the third unramified cohomology for a large class of rationally chain connected threefolds over finite fields, confirming a conjecture of Colliot-Thelene and Kahn. This is a joint work with Federico Scavia.
Link:
Workshop: