In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively...

} The norm residue isomorphism theorem, proved around 2000 by Vladimir Voevodsky, relates this to Galois cohomology by means of an isomorphism K n M (...

to 3 modulo 4), then the residue class field has p2 elements, and it is an extension of degree 2 (unique, up to an isomorphism) of the prime field with...

as of September 2022[update]. The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic...

R_{n,F}(\{a,b\})} . Because of the norm residue isomorphism theorem, R n , F {\displaystyle R_{n,F}} is an isomorphism and the n {\displaystyle n} -torsion...

Cantor's isomorphism theorem (order theory) Dilworth's theorem (combinatorics, order theory) Four functions theorem (combinatorics) Hahn embedding theorem (ordered...

a century. Alexander Merkurjev and Andrei Suslin prove the norm residue isomorphism theorem in Milnor K2-theory for the case n = 2 and ℓ arbitrary, with...

to higher torsion as the Merkurjev–Suslin theorem. The full statement of the norm residue isomorphism theorem (also known as the Bloch-Kato conjecture)...

of 4. In fact from the Kummer–Vandiver conjecture and the norm residue isomorphism theorem follow a full conjectural calculation of the K-groups for all...

Conjecture by Charles Weibel" (PDF). ICTP SMR/1840-9. The norm residue isomorphism theorem, Journal of Topology, Volume 2, 2009, pp. 346–372 List of Fellows...

maps called the local Artin symbol, the local reciprocity map or the norm residue symbol θ v : K v × / N L v / K v ( L v × ) → G ab , {\displaystyle \theta...

is a consequence of the norm residue isomorphism theorem. Namely, the Beilinson-Lichtenbaum conjecture (Voevodsky's theorem) says that for a smooth scheme...

proof of this conjecture in 2009; the result is now called the norm residue isomorphism theorem. Mazza, Carlo; Voevodsky, Vladimir; Weibel, Charles (2006)...

by Wau Holland and others. Alexander Merkurjev proves the norm residue isomorphism theorem for the case n = 2 and ℓ = 2. April 26 – Dr. Michael R. Harrison...

is simply zero, or in case the region includes singularities, the residue theorem computes the integral in terms of the singularities. This also implies...

{\displaystyle N_{L/F}} denotes the idelic norm map from L to F. This isomorphism is named the reciprocity map. The existence theorem states that the reciprocity map...

a ring isomorphism from the field of complex numbers to the ring of these matrices, proving that these matrices form a field. This isomorphism associates...

effective. For example, in modular arithmetic, the canonical form for a residue class is usually taken as the least non-negative integer in it. Operations...

G^{\text{ab}},} called the local Artin symbol, the local reciprocity map or the norm residue symbol. Let L/K be a Galois extension of global fields and CL stand for...

mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often...

extension L of K the reciprocity map induces an isomorphism of the quotient group K×/N(L×) of K× by the norm group N(L×) of the extension L× to the Galois...

with respect to a metric induced by a discrete valuation v and if its residue field k is finite. In general, a local field is a locally compact topological...

{\displaystyle K} results in an isomorphism E ≅ K n . {\displaystyle E\cong K^{n}.} Therefore fixing a basis induces an isomorphism ( A K ) n ≅ A E . {\displaystyle...

the norm residue group by the unit groups under the Artin isomorphism. The image of G n ( L / K ) {\displaystyle G^{n}(L/K)} under the isomorphism G (...

Hilbert's ninth problem: find the most general reciprocity law for the norm residues of k {\displaystyle k} -th order in a general algebraic number field...

reformulated the reciprocity laws as saying that a product over p of Hilbert norm residue symbols (a,b/p), taking values in roots of unity, is equal to 1. Artin...

deeper result, the Bloch-Kato conjecture (also called the norm residue isomorphism theorem), relates Milnor K-theory to Galois cohomology or étale cohomology:...

end of the nineteenth century, Ludwig Stickelberger obtained his theorem on the residue of the discriminant modulo four. The discriminant defined above...

is a maximal ideal, since the residue field C(X)/ker evp is the field of real numbers, by the first isomorphism theorem. A topological space X is pseudocompact...

theorems in algebra. For example, Witt's decomposition theorem says that a nondegenerate quadratic form over a field is determined up to isomorphism by...