Citations
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Journal ArticleDOI
Class fields of abelian extensions of Q.
Barry Mazur,Andrew Wiles +1 more
TL;DR: In this article, a study of abelian varieties which are good quotients of Jz (N) is presented, where the kernel of the Eisenstein ideal is considered.
Journal ArticleDOI
K-cohomology of Severi-Brauer Varieties and the norm residue homomorphism
A S Merkur'ev,Andrei Suslin +1 more
TL;DR: In this article, it was shown that for any field of characteristic prime to, if, then any central simple algebra of exponent is similar to a tensor product of cyclic algebras, then the Gersten spectral sequence is degenerate.
Journal ArticleDOI
Motivic cohomology with $\mathbf {Z}/2$-coefficients
Book
Central Simple Algebras and Galois Cohomology
Philippe Gille,Tamás Szamuely +1 more
TL;DR: The first comprehensive introduction to the theory of central simple algebras over arbitrary fields was given by Brauer, Noether, Hasse and Albert as mentioned in this paper, who also gave a proof of the Merkurjev-Suslin theorem.
Book
Lectures on Algebraic Cycles
TL;DR: The theory of algebraic cycles encompasses such central problems in mathematics as the Hodge conjecture and the Bloch-Kato conjecture on special values of zeta functions as discussed by the authors, and it has remained influential and is still the best place to learn the guiding philosophy of algebraIC cycles and motives.
References
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Book
A Course in Arithmetic
TL;DR: In this article, the theorem on arithmetic progressions modular forms is proved for finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratics forms with discriminant +-1.
Book
Basic Number Theory
TL;DR: In this article, the authors define a classfield theory for algebraic number-fields with respect to simple algebras over A-fields and the Brauer group of a local field.
Journal ArticleDOI
Algebraic K-theory and quadratic forms
TL;DR: In this paper, the authors define a graded ring K, F associated to any rational function field F and construct a homomorphism associated with a discrete valuation on F with residue class field F.