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On Algorithmic Aspects of the -Torsion of Brauer Groups


Lin Wang
Mao-Zhi Xu

Abstract

We study the algorithmic aspects of the ℓ-torsion of the Brauer group Br(K) of a eld K which contains the ℓ-th roots of unity μℓ, only provided with basic operations on the elements of K. We use a primitive root of unity and nonzero elements in K to represent elements of Br(K)[ℓ]. An algorithm is given to compute the invariant homomorphism on Br(Qℓ(μℓ))[ℓ] for an odd prime ℓ. We also give a remark on potential application of Brauer groups to solve the discrete logarithm problem of multiplicative groups of nite fields.

Quaestiones Mathematicae 35(2012), 297-312

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606