Geometric Langlands correspondence for classical Lie groups over global function fields

What the research examines

This work proves the unramified geometric Langlands conjecture for classical orthogonal and symplectic groups over algebraic curves defined over finite fields, constructing an equivalence between derived categories of automorphic D-modules and coherent sheaves.

Why it may matter

One of the grandest triumphs in modern pure mathematics, harmonizing algebraic number theory, representation theory, and string dualities.

What to examine carefully

Extending categorical equivalences to wild ramification and singular spectral stacks requires non-trivial derived geometry extensions.

Try a small, reproducible follow-up

Examine the geometric Langlands correspondence for GL(1) and illustrate how it reduces to the classical geometric Class Field Theory.

Questions to investigate

1. How does the vanishing of the Whittaker coefficient sheaf guarantee full faithfulness of the functor?
2. What geometric structures on the stack of flat connections match the spectral side decomposition?

These are independently proposed educational investigations, not activities that the original research authors claim to have completed.

Publication & researcher information

Multi-author research may involve universities in several countries. Unverified institutions and contact addresses are not inferred from authors' names.

Primary sources