Displaying similar documents to “On the composition of nondegenerate quadratic forms with an arbitrary index”

Hurwitz pairs and Clifford valued inner products

Jan Cnops (1996)

Banach Center Publications

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After an overview of Hurwitz pairs we are showing how to actually construct them and discussing whether, for a given representation, all Hurwitz pairs of the same type are equivalent. Finally modules over a Clifford algebra are considered with compatible inner products; the results being then aplied to Hurwitz pairs.

Excellent connections in the motives of quadrics

Alexander Vishik (2011)

Annales scientifiques de l'École Normale Supérieure

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In this article we prove the conjecture claiming that the motive of a real quadric is the “most decomposable” among anisotropic quadrics of given dimension over fields. This imposes severe restrictions on the motive of arbitrary anisotropic quadric. As a corollary we estimate from below the rank of indecomposable direct summand in the motive of a quadric in terms of its dimension. This generalizes the well-known Binary Motive Theorem. Moreover, we have the description of the Tate motives...

On the computation of quadratic 2 -class groups

Wieb Bosma, Peter Stevenhagen (1996)

Journal de théorie des nombres de Bordeaux

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We describe an algorithm due to Gauss, Shanks and Lagarias that, given a non-square integer D ≡ 0 , 1 mod 4 and the factorization of D , computes the structure of the 2 -Sylow subgroup of the class group of the quadratic order of discriminant D in random polynomial time in log D .