Q. Which one of the following statements correctly defines the Riemann–Hilbert correspondence?

[A] It provides a duality between analytic solutions of differential equations and holomorphic functions on compact manifolds.

[B] It establishes an equivalence between the category of flat connections on complex algebraic varieties and the category of local systems, relating systems of differential equations to their monodromy representations.

[C] It is a method in geometry for constructing projective varieties from Kähler manifolds.

[D] It describes a canonical morphism between the fundamental groups of differentiable and algebraic varieties.

Answer: B
Notes:

Explanation: It establishes an equivalence between the category of flat connections (regular holonomic D-modules) on complex algebraic varieties and the category of local systems (or perverse sheaves), relating systems of differential equations to their monodromy representations.

Source: TH

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