Section
Modern Langlands dependency closure index
The reusable arithmetic, representation-theoretic, geometric, and categorical prerequisites added by the semantic closure audit of the modern Langlands collection.
Core idea
This index records the 57 reusable prerequisite knowls added after a page-by-page semantic audit of the modern Langlands collection and the rewritten Langlands Letter vocabulary. They complement the campaign's subject pages in the modern Langlands foundations index.
The audit compared mathematical meaning rather than filenames or exact title strings. Narrow notation and convention choices remain defined in their consuming pages; the entries below are concepts useful across more than one page.
Arithmetic, ramification, and p-adic Hodge theory
- Decomposition group
- Inertia subgroup
- Local class field theory
- Chebotarev density theorem
- Fontaine period rings
- Hodge–Tate representation
- De Rham Galois representation
- Crystalline Galois representation
- Semistable Galois representation
- Artin conductor
The existing Frobenius endomorphism page was also extended to distinguish field Frobenius, absolute Frobenius, and relative Frobenius instead of creating a competing page.
Reductive groups and local topology
Harmonic analysis and p-adic representation theory
- Test-function space on a local group
- Distribution on a local group
- Jacquet module
- Parabolic modulus character
- Tempered representation of a p-adic group
- Langlands classification for p-adic groups
- Bernstein decomposition
- Bernstein center
- Central character
- Harish–Chandra character of a p-adic representation
- Local epsilon factor
- Local gamma factor
Global automorphic analysis
Endoscopy and the geometry of orbital integrals
Function fields and étale cohomology
Perfectoid, local Shimura, and categorical foundations
Reading strategy
Start from a subject page in the modern foundations index and follow only the dependencies needed for that page. The short first section of each knowl gives the canonical definition; progressive sections record conventions, examples, scope boundaries, and literature without making the initial reading path unnecessarily long.