Perspectivas Matemáticas

The Hodge conjecture is at the confluence of three major areas of mathematics, namely, Hodge theory, motivic cohomology, and arithmetic geometry. Hodge never really stated this as a conjecture, but rather an important open problem. Over the past 60 years, little progress has been made on this conjecture. Based on some ideas of A. Beilinson, we present a modern version of this conjecture involving the higher algebraic K-groups, in the hope that this will inspire others to do the same. This talk is aimed at a general audience.