Algebraic Cycles and Etale Cohomology

This lecture discusses the concept of algebraic cycles and etale cohomology, exploring how they are related and the implications of certain counterexamples. The instructor presents examples of counterexamples to the Hodge conjecture, highlighting the importance of understanding torsion classes and their relationship to etale cohomology. The lecture delves into the complexities of lifting torsion classes and the challenges in obtaining explicit descriptions of certain classes in etale cohomology groups.