Displaying similar documents to “Spinor genera under field extensions, I”

Applications of spinor class fields: embeddings of orders and quaternionic lattices

Luis Arenas-Carmona (2003)

Annales de l'Institut Fourier

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We extend the theory of spinor class fields and relative spinor class fields to study representation problems in several classical linear algebraic groups over number fields. We apply this theory to study the set of isomorphism classes of maximal orders of central simple algebras containing a given maximal Abelian suborder. We also study isometric embeddings of one skew-Hermitian Quaternionic lattice into another.

Maximal unramified extensions of imaginary quadratic number fields of small conductors, II

Ken Yamamura (2001)

Journal de théorie des nombres de Bordeaux

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In the previous paper [15], we determined the structure of the Galois groups Gal ( K u r / K ) of the maximal unramified extensions K u r of imaginary quadratic number fields K of conductors 1000 under the Generalized Riemann Hypothesis (GRH) except for 23 fields (these are of conductors 723 ) and give a table of Gal ( K u r / K ) . We update the table (under GRH). For 19 exceptional fields K of them, we determine Gal ( K u r / K ) . In particular, for K = 𝐐 ( - 856 ) , we obtain Gal ( K u r / K ) S 4 ˜ × C 5 and K u r = K 4 , the fourth Hilbert class field of K . This is the first example of a number...