Zero-cycles on hypersurfaces of low degree
Northeastern University, Boston, U.S.A.
Algebraic cycles give an algebraic geometers' version of cohomology. Although this was first exploited by Grothendieck and others, Bloch and Srinivas made precise how algebraic decompositions of the diagonal cycle in X x X has striking consequences for the cohomology of X. We will illustrate this by showing how Roitman's theorem on the triviality of 0-cycles on hypersurfaces of low degree leads to congruences mod q for the number of solutions of low-degree equations over a field with q elements.