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...

Hodge–Tate module is an analogue of a Hodge structure over p-adic fields. Serre (1967) introduced and named Hodge–Tate structures using the results of Tate (1967)...

John Torrence Tate Jr. (March 13, 1925 – October 16, 2019) was an American mathematician distinguished for many fundamental contributions in algebraic...

determined up to isogeny by the Galois representation on its Tate module H1(Aks, Zℓ). The Tate conjecture also holds for K3 surfaces over finitely generated...

Mumford's construction for Hodge–Tate modules, using the work of Tate (1967) on p-divisible groups, and named them Mumford–Tate groups. The algebraic torus...

sheaves of coefficients can be predicted (via Galois cohomology and Tate modules). For any scheme X the category Et(X) is the category of all étale morphisms...

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...

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 Tate modules of...

elementary Tate modules 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 Tate module Tℓ(E) of the elliptic curve E (the inverse limit of the ℓn-torsion points) to the Tate module Tℓ(μ) of the multiplicative...

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 Tate modules as Galois modules. It also makes them harder to deal with in terms of the conjectural algebraic geometry (Hodge conjecture and Tate conjecture)...

Frobenius endomorphism on the first cohomology group or Tate module) have absolute value √q. Tate (1966) showed that the map taking an isogeny class to...

only if the ℓ-adic Tate module Tℓ of A is unramified. Andrew Ogg (1967) introduced the criterion for elliptic curves. Serre and Tate (1968) used the results...

Tate's isogeny theorem, proved by Tate (1966), states that two abelian varieties over a finite field are isogeneous if and only if their Tate modules...

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...

posted a preprint (Skinner & Urban 2010). Ferrero–Washington theorem Tate module of a number field Sources Coates, J.; Sujatha, R. (2006), Cyclotomic...

especially the theory of automorphic forms, through the notions of elliptic module and the theory of the geometric Langlands correspondence. Drinfeld introduced...

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...

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...

{\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...

Jean-Pierre Serre and John Tate's study of Tate modules of abelian varieties and the notion of Hodge–Tate representation. Hodge–Tate representations are related...

ℓ-adic representations. The p-adic cyclotomic character is the p-adic Tate module of the multiplicative group scheme Gm,Q over Q. As such, its representation...

theorem that abelian varieties with isomorphic Tate modules (as Q ℓ {\displaystyle \mathbb {Q} _{\ell }} -modules with Galois action) are isogenous. A sample...

mathematics, a Koszul–Tate resolution or Koszul–Tate complex of the quotient ring R/M is a projective resolution of it as an R-module which also has a structure...

Hodge star operator Hodge structure Mixed Hodge structure Hodge–Tate module Hodge theory Mixed Hodge module Hodge–Arakelov theory p-adic Hodge theory...

group by taking the direct sum of the Witt vector cohomology and the Tate module of the Picard variety. Serre, J.P. (1958), "Sur la topologie des variétés...

module satisfying certain conditions. Class formations were introduced by Emil Artin and John Tate to organize the various Galois groups and modules that...

abelian p-extension of K ^ {\displaystyle {\hat {K}}} by A(p). Let the Tate module T p ( K ) = G a l ( A ( p ) / K ^ )   . {\displaystyle T_{p}(K)=\mathrm...

compositum of all fields formed by adjoining such modules to the original field gives the ramified part. A Lubin–Tate extension of a local field K is an abelian...