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Structs§
- Abelian
Variety - An abelian variety over a field k of dimension g.
- Absolute
Height - Absolute Weil height H(P) on projective space.
- Automorphic
Representation - An automorphic representation π = ⊗_v π_v.
- Berkovich
Space - A Berkovich space M(A) represented by a finite list of seminorm data.
- Birch
Swinnerton Dyer Data - Data for the Birch and Swinnerton-Dyer conjecture.
- Canonical
Model - Canonical model of a Shimura variety over its reflex field.
- Chow
Group - A Chow group CH^n(X) of codimension-n algebraic cycles modulo rational equivalence.
- Condensed
Abelian Group - A condensed abelian group: a sheaf of abelian groups on the category of profinite sets.
- Dual
Abelian Variety - The dual abelian variety A^ = Pic^0(A).
- Elliptic
Curve - An elliptic curve E: y² = x³ + ax + b over a field k.
- Faltings
Thm - Faltings’s theorem (Mordell conjecture): curves of genus ≥ 2 have finitely many rational points.
- Galois
Representation - A continuous Galois representation ρ: G_K → GL_n(R).
- Height
Function - The canonical Néron-Tate height ĥ: E(K̄) → ℝ.
- Isogeny
- An isogeny φ: E → E’ (group homomorphism with finite kernel).
- Langlands
Correspondence - The Langlands correspondence ρ_π ↔ π.
- Logarithmic
Height - Logarithmic (Weil) height h(P) = log H(P).
- Nearly
Ordinary Representation - A nearly ordinary p-adic Galois representation (Borel reduction at p).
- Neron
Model - A Néron model data record for an abelian variety A over the fraction field of a DVR.
- Northcott
Property - The Northcott property: finitely many points of bounded height.
- Perfectoid
Field - A perfectoid field K with its residue characteristic p.
- Polarized
Abelian Variety - A polarized abelian variety: (A, λ) where λ: A → A^ is an isogeny from A to its dual.
- Shimura
Datum - A Shimura datum (G, X).
- Shimura
Variety - A Shimura variety Sh_K(G, X) as a moduli space.
- Tate
Module - The p-adic Tate module T_p(A) = lim A[p^n].
- Tolimani
Conjecture - Status record for the André-Oort conjecture (Tolimani’s theorem).
- Torsion
Point - The n-torsion subgroup E[n] ⊂ E.
Enums§
- Langlands
Type - Type of Langlands correspondence.
- Neron
Reduction Type - Reduction type of the special fiber of a Néron model.