Algebraic Cycles and the Weil Conjectures

摘要

With the development of the l-adic etale cohomology, Weil's conjectures about the geta function have been reduced to formal consequences of certain basic conjectures in the theory of algebraic cycles. This formalism is reviewed in this report. It is decided to work over a fixed algebraically closed field k, to let variety mean integral algebraic k-scheme and to assume all varieties smooth, closed subschemes of given projective spaces. (Author)