nLab categorical geometric Langlands conjecture

The categorical geometric Langlands conjecture is a categorical version of the geometric Langlands conjecture. It is formulated as an equivalence of stable (infinity,1)-categories of

• D-modules on the derived stack of G-bundles on a curve $X$,

and

• ind-coherent sheaves on the derived stack of $G^\vee$-equivariant local systems on $X$,

where $X$ is a smooth complete curve over a field of characteristic zero, and $G$ is a reductive group and $G^\vee$ is its Langlands dual.

References

• Gurbir Dhillon, An informal introduction to categorical representation theory and the local geometric Langlands program (arXiv:2205.14578)

• Dennis Gaitsgory, Notes on geometric Langlands, web.

• D. Gaitsgory, N. Rozenblyum, A study in derived algebraic geometry.

• D. Gaitsgory et. al., Geometric representation theory, graduate seminar, Fall 2009–Spring 2010, web.

• MO/56571, A precise statement of the categorical version of geometric Langlands conjecture.