Just For Fun Quiz / Number Theory

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Equivalence class of Galois representations
Lift from modular forms to Siegel modular forms
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
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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