Beilinson conjectures

Beilinson's conjectures propose deep relationships between the values of special functions called L-functions, linked to algebraic objects like numbers and geometric shapes, and the geometric and algebraic properties of those objects. They suggest that these special values encode important information about the structure and symmetries of mathematical entities, connecting analysis, algebra, and geometry. In essence, the conjectures predict precise formulas relating complex analytical data to algebraic invariants, shedding light on fundamental patterns in number theory and arithmetic geometry.