Module associated to an abelian variety on which an absolute Galois group acts in order to obtain an l-adic representation

The Galois group of the maximal abelian unramified p-extension of a number field K over K is canonically isomorphic to the Sylow p-subgroup of the

Orthogonal complement of the space of Eisenstein series under the Petersson inner product

Type of Z_p extension contained in the field obtain by adjoining all p-power roots of unity

Galois groups of abelian extensions correspond to closed subgroups of what group

Type of function the can be defined by interpolation or by lambda-modules

Theorem that states that every abelian extension of Q is a subfield of a Cyclotomic Field

The Langlands Program relates Galois representations to

Hints

Conjecture that connects K-theory to Etale cohomology

Category constructed to have a 'universal' cohomology

Langlands and Tunnel proved that the residual 3-adic Galois represesntation associated to an Elliptic Curve is Modular if it is

Type of ideal that is related to p-adic L-functions in Iwasawa Theory

The Hecke Algebra is generated by the Hecke Operators corresponding to primes and the

Group whose pieces measures the obstruction to a piece of a Selmer group being canonically isomorphic to the corresponding Selmer Group

Image of the uniformizer under the Local Artin Reciprocity Map

Conjecture asserting that for a given prime p, p does not divide the class number of the maximal totally real subfield of the cyclotomic field obtain by adjoining the pth roots of

Theorem about the density of primes who map to a certain Galois conjugacy class under the Artin Reciprocity Map

Herbrand and Ribet related the non-vanishing of certain pieces of ideal class groups obtain from orthogonal idempotents of the group ring to the p-divisibility of

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