Lefschetz standard conjecture

The Lefschetz standard conjecture is a mathematical prediction related to the geometry of algebraic varieties (geometric objects defined by polynomial equations). It suggests that certain natural transformations—called Lefschetz operators—arising from geometric intersections, are algebraic in nature, meaning they can be described by algebraic cycles. Essentially, the conjecture proposes that the deep geometric symmetries and properties of these varieties are reflected through explicit algebraic structures, supporting a profound connection between geometry and algebra. This conjecture remains unproven in general but is fundamental to understanding the relationship between topology, geometry, and algebraic cycles in mathematics.