Research proof index

Hecke operators are preserved under the identification 𝒮²(U, χ; M ⊗ N) ≃ M ⊗ 𝒮²(U, χ; N).

Let R₀ be a topological ring, topologically of finite type (over ℤ). Consider a family of (cardinality) finite rings R i with the discrete topology whose cardinalites are unifomly bounded. Given a family of continuous ring homs f i : R →+* R i, the lift R →+* 𝒰(Rᵢ) is also continuous.

Let R₀ be a topological ring, topologically of finite type (over ℤ). Consider a family of (cardinality) finite continuous R₀-algebras R i with the discrete topology whose cardinalites are unifomly bounded. Then 𝒰(Rᵢ) ≃ₐ[R] R i for F-many i.

Let R₀ be a topological ring, topologically of finite type (over ℤ). Consider a family of (cardinality) finite rings R i with the discrete topology whose cardinalites are unifomly bounded. Given a family of continuous ring homs f i : R →+* R i, there exists F-many i such that 𝒰(Rᵢ) ≃+* R i and this map is compatible with f.

Let R₀ be a topological ring, topologically of finite type (over ℤ). Consider a family of (cardinality) finite rings R i with the discrete topology whose cardinalites are unifomly bounded. Given a family of continuous surjective ring homs f i : R →+* R i, the lift R →+* 𝒰(Rᵢ) is also surjective.

The rational points of the quadratic twist, viewed inside E(L) via the isomorphism over L, are exactly the points of E(L) on which the nontrivial element of Gal(L/K) acts as -1 (just as E(K) consists of the points on which it acts as +1). One inclusion is Affine.Point.map_baseChange (the base change of a K-point is σ-fixed) together wi...