In mathematics, a Galois module is a G -modulewith G being the Galois group of some extension of fields. The term Galois representation is frequently used when the G -module is a vector space over a field or a free module over a ring in representation theory, but can also be used as a synonym for G -module. The study of Galois modules for extensions of local or global fields and their group cohomology is an important tool in number theory.
In mathematics, complex multiplication CM is the theory of elliptic curves E that have an endomorphism ring larger than the integers; and also the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense.
Put another way, it contains the theory of elliptic functions with extra symmetries, such as are visible when the period lattice is the Gaussian integer Stronger - Shimura Curves - Play Truck (CDr) or Eisenstein integer lattice. In number theory, a branch of mathematics, a cusp form is a particular kind of modular form with a zero constant coefficient in the Fourier series expansion.
In mathematics, the Hasse—Weil zeta function attached to an algebraic variety V defined over an algebraic number field K is one of the two most important types of L-function. Such L -functions are called 'global', in that they are defined as Euler products in terms of local zeta functions. They form one of the two major classes of global L -functions, the other being the L -functions associated to automorphic representations.
Conjecturally, there is just one essential type of global L -function, with two descriptions ; this would be a vast generalisation of the Taniyama—Shimura conjecture, itself a very deep and recent result in number theory.
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.
These functions were introduced in by Emil Artin, in connection with his research into class field theory. Their Stronger - Shimura Curves - Play Truck (CDr) properties, in particular the Artin conjecture described below, have turned out to be resistant to easy proof. One of the aims of proposed non-abelian class Stronger - Shimura Curves - Play Truck (CDr) theory is to incorporate the complex-analytic nature of Artin L -functions into a larger framework, such as is provided by automorphic forms and the Langlands program.
So far, only a small part of such Stronger - Shimura Curves - Play Truck (CDr) theory has been put on a firm basis. In mathematics, a Drinfeld module is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing the Carlitz module.
Loosely speaking, they provide a function field analogue of complex multiplication theory. A shtuka is a sort of generalization of a Drinfeld module, consisting roughly of a vector bundle over a curve, together with some extra structure identifying a "Frobenius twist" of the bundle with a "modification" of it.
In mathematics, a Weil groupintroduced by Weilis a modification of the absolute Galois group of a local or global field, used in class field theory.
For such a field Fits Weil group is generally denoted W F. In mathematics, the local Langlands conjecturesintroduced by Robert Langlands, are part of the Langlands program. They describe a correspondence between the complex representations of a reductive algebraic group G over a local field Fand representations of the Langlands group of F into the L-group of G.
This correspondence is not a bijection in general. The conjectures can be thought of as a generalization of local class field theory from abelian Galois groups to non-abelian Galois Stronger - Shimura Curves - Play Truck (CDr). In number theory, the Eichler—Shimura congruence relation expresses the local L -function of a modular curve at a prime p in terms of the eigenvalues of Hecke operators.
It was introduced by Eichler and generalized by Shimura Roughly speaking, it says that the correspondence on the modular curve inducing the Hecke operator T p is congruent mod p to the sum of the Frobenius map Frob and its transpose Ver. In other words. In Borel, Armand ; Casselman, William eds. Shipped From. Joined Reverb.
Message Seller. About This Listing. Made in Japan in Fujigen plant for Shimamura guitar store. Part of this guitar are made with Heritage Wood: Made in going by serial Body Stronger - Shimura Curves - Play Truck (CDr) Curly Maple on heritage wood hard maple Body Back: 2 piece Mahogany Neck: 1 piece mahogany 18 degree head angle Rosewood fingerboard Set neck with heelless deep joint C.
One of the knobs has cracks inside it. Nothing major. Reviews of this Shop. They form Team Sacred Treasureswhose endings often entail the canon events of any parties involved. At the initial stages of development, she was referred to as the "Bell Girl," but before long she received the nickname of "Yuna" then finally receive the more appropriate name that she has now.
Unlike the other members of the Sacred Treasures, Chizuru is well-mannered individual who speaks in a calm and collected tone. She'll do whatever she can to keep Orochi sealed, even going as far as using The King of Fighters tournaments to bring the other two Sacred Treasures together, even without their consent.
However, when her powers were taken, her will to fight was taken along with it. Her fighting style is very soft, with moves that resemble traditional Japanese dancing.
She employs her mirror images to perfection, using them to surprise and confuse her opponents.
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