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Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree

Nazar Arakelian, Herivelto Borges (2015)

Acta Arithmetica

For each integer s ≥ 1, we present a family of curves that are q -Frobenius nonclassical with respect to the linear system of plane curves of degree s. In the case s=2, we give necessary and sufficient conditions for such curves to be q -Frobenius nonclassical with respect to the linear system of conics. In the q -Frobenius nonclassical cases, we determine the exact number of q -rational points. In the remaining cases, an upper bound for the number of q -rational points will follow from Stöhr-Voloch...

Graded quaternion symbol equivalence of function fields

Przemysław Koprowski (2007)

Czechoslovak Mathematical Journal

We present criteria for a pair of maps to constitute a quaternion-symbol equivalence (or a Hilbert-symbol equivalence if we deal with global function fields) expressed in terms of vanishing of the Clifford invariant. In principle, we prove that a local condition of a quaternion-symbol equivalence can be transcribed from the Brauer group to the Brauer-Wall group.

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