In mathematics, a Tate module of an abelian group, named for John Tate, is a module constructed from an abelian group A. Often, this construction is made in the following situation: G is a commutative group scheme over a field K, Ks is the separable closure of K, and A = G(Ks) (the Ks-valued points of G). In this case, the Tate module of A is equipped with an action of the absolute Galois group of K, and it is referred to as the Tate module of G.
In mathematics, a Tatemodule of an abelian group, named for John Tate, is a module constructed from an abelian group A. Often, this construction is made...
Zℓ-module (where Zℓ is the integral closure of Zℓ in Qℓ). The first examples to arise were the ℓ-adic cyclotomic character and the ℓ-adic Tatemodules of...
number theory and algebraic geometry, the Tate twist, named after John Tate, is an operation on Galois modules. For example, if K is a field, GK is its...
their Tatemodules as Galois modules. It also makes them harder to deal with in terms of the conjectural algebraic geometry (Hodge conjecture and Tate conjecture)...
elementary Tatemodules to be topological R-modules of the form P ⊕ Q ∗ {\displaystyle P\oplus Q^{*}} where P and Q are projective R-modules (of possibly...
Tℓ(E) → Tℓ(μ) on the Tatemodule Tℓ(E) of the elliptic curve E (the inverse limit of the ℓn-torsion points) to the Tatemodule Tℓ(μ) of the multiplicative...
In Galois cohomology, local Tate duality (or simply local duality) is a duality for Galois modules for the absolute Galois group of a non-archimedean local...
{\displaystyle p:X\to \{pt\}} . One of the first mixed Hodge modules available is the weight 0 Tate object, denoted Q _ X H d g {\displaystyle {\underline {\mathbb...
posted a preprint (Skinner & Urban 2010). Ferrero–Washington theorem Tatemodule of a number field Sources Coates, J.; Sujatha, R. (2006), Cyclotomic...
projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, keeping some of the main properties of free modules. Various...
determined up to isogeny by the Galois representation on its Tatemodule H1(Aks, Zℓ). The Tate conjecture also holds for K3 surfaces over finitely generated...
They were introduced by John Tate (1952, p. 297), and are used in class field theory. If G is a finite group and A a G-module, then there is a natural map...
ℓ-adic representations. The p-adic cyclotomic character is the p-adic Tatemodule of the multiplicative group scheme Gm,Q over Q. As such, its representation...
especially the theory of automorphic forms, through the notions of elliptic module and the theory of the geometric Langlands correspondence. Drinfeld introduced...
In mathematics, Tate duality or Poitou–Tate duality is a duality theorem for Galois cohomology groups of modules over the Galois group of an algebraic...
group by taking the direct sum of the Witt vector cohomology and the Tatemodule of the Picard variety. Serre, J.P. (1958), "Sur la topologie des variétés...
known to be underlain by a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James Lepowsky...
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