The geometric Langlands correspondence relates sheaves on a moduli stack of principal bundles on an algebraic curve to spectral objects built from local systems for the Langlands dual group. Its eigensheaf formulation realizes a dual-group local system as the eigenvalue of geometric Hecke operators. Its categorical formulations compare whole categories and include prescribed nilpotent singular-support conditions. The restricted positive-characteristic formulation uses the restricted local-system stack, defined using tensor functors into the chosen category of lisse sheaves, rather than a de Rham moduli problem.
Geometric Langlands Correspondence
See also
Algebraic Stack, Global Nilpotent Cone, Hecke Eigensheaf, Langlands Dual Group, Langlands Program, Local System, Nilpotent Cone, Perverse Sheaf, Principal Bundle, Quantum Geometric Langlands Correspondence, Reductive GroupExplore with Wolfram|Alpha
References
Arinkin, D.; Gaitsgory, D.; Kazhdan, D.; Raskin, S.; Rozenblyum, N.; and Varshavsky, Y. "The Stack of Local Systems with Restricted Variation and Geometric Langlands Theory with Nilpotent Singular Support." 5 Oct 2020. https://arxiv.org/abs/2010.01906.Cite this as:
Weisstein, Eric W. "Geometric Langlands Correspondence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeometricLanglandsCorrespondence.html