Tractable Fields

Chacron, Maurice J.; Tignol, Jean-Pierre; Wadsworth, Adrian R.

doi:10.4153/cjm-1999-002-0

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Appendix: Tractable Fields1

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Cited by 3 publications

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“…The converse of Proposition 10.1 is false. For every odd prime p, Q p ((x)) is tractable by [CTW,Prop. 2.5].…”

Section: Appendix: Tractable Fieldsmentioning

confidence: 99%

Quaternion Algebras with the Same Subfields

Garibaldi

Saltman

2010

Quadratic Forms, Linear Algebraic Groups, and Cohomology

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Abstract. G. Prasad and A. Rapinchuk asked if two quaternion division F -algebras that have the same subfields are necessarily isomorphic. The answer is known to be "no" for some very large fields. We prove that the answer is "yes" if F is an extension of a global field K so that F/K is unirational and has zero unramified Brauer group. We also prove a similar result for Pfister forms and give an application to tractable fields.

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“…The converse of Proposition 10.1 is false. For every odd prime p, Q p ((x)) is tractable by [CTW,Prop. 2.5].…”

Section: Appendix: Tractable Fieldsmentioning

confidence: 99%

Quaternion Algebras with the Same Subfields

Garibaldi

Saltman

2010

Quadratic Forms, Linear Algebraic Groups, and Cohomology

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Tractability of Algebraic Function Fields in One Variable of Genus Zero Over Global Fields

Han

2001

Journal of Algebra

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Tractability of algebraic function fields in one variable of genus one over global fields

Han

2007

Journal of Algebra

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A field k of characteristic unequal to 2 is called tractable if for every nonzero a i , b i ∈ k, i = 1, 2, 3, whenever the quaternion algebra (a i , b j /k) is split for all i = j and (a 1 , b 1 /k) ∼ = (a 2 , b 2 /k) ∼ = (a 3 , b 3 /k), then (a i , b i /k) is split. In the present paper, we study tractability of algebraic function fields in one variable over global fields and give specific examples of tractable function fields and intractable function fields of genus one over Q, the rationals.

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Tractable Fields

Cited by 3 publications

References 16 publications

Quaternion Algebras with the Same Subfields

Quaternion Algebras with the Same Subfields

Tractability of Algebraic Function Fields in One Variable of Genus Zero Over Global Fields

Tractability of algebraic function fields in one variable of genus one over global fields

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