Langlands Program

Reciprocity between Galois representations and automorphic forms.

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Langlands Program. Reciprocity between Galois representations and automorphic forms.

Foundations and canonical references

The standard treatments of langlands program approach the subject from complementary angles. Bernstein, An Introduction to the Langlands Program (2003) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.

Open methodological questions for langlands program include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2003
    An Introduction to the Langlands Program
    bernstein-2003, gelbart-2003

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  1. 01

    Automorphic Forms

    Cusp forms on adelic groups and the trace formula.
  2. 02

    Geometric Langlands

    Categorical and geometric reformulations of Langlands correspondences.

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