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A Weak Hasse Principle for Central Simple Algebras with an Involution

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2001

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Lewis, David W.
Unger, Thomas

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HOFFMAN, J. William, ed. and others. Proceedings of the Conference on Quadratic Forms and Related Topics : Baton Rouge, Louisiana, USA ; March 26 - 30, 2001. Bielefeld, 2001, pp. 241-251. Documenta mathematica. 2001,1

Zusammenfassung

The notions of totally indefinite and weakly isotropic algebras with involution are introduced and a proof is given of the fact that a field satisfies the Effective Diagonalization Property (ED) if and only if it satisfies the following weak Hasse principle: every totally indefinite central simple algebra with involution of the first kind over the given field is weakly isotropic. This generalizes a known result from quadratic form theory.

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Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Real fields, central simple algebras, involutions, weak Hasse principles, hermitian squares

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Quadratic Forms and Related Topics, 26. März 2001 - 30. März 2001, Baton Rouge, Louisiana, USA
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ISO 690LEWIS, David W., Claus SCHEIDERER, Thomas UNGER, 2001. A Weak Hasse Principle for Central Simple Algebras with an Involution. Quadratic Forms and Related Topics. Baton Rouge, Louisiana, USA, 26. März 2001 - 30. März 2001. In: HOFFMAN, J. William, ed. and others. Proceedings of the Conference on Quadratic Forms and Related Topics : Baton Rouge, Louisiana, USA ; March 26 - 30, 2001. Bielefeld, 2001, pp. 241-251. Documenta mathematica. 2001,1
BibTex
@inproceedings{Lewis2001Hasse-23583,
  year={2001},
  title={A Weak Hasse Principle for Central Simple Algebras with an Involution},
  number={2001,1},
  address={Bielefeld},
  series={Documenta mathematica},
  booktitle={Proceedings of the Conference on Quadratic Forms and Related Topics : Baton Rouge, Louisiana, USA ; March 26 - 30, 2001},
  pages={241--251},
  editor={Hoffman, J. William},
  author={Lewis, David W. and Scheiderer, Claus and Unger, Thomas}
}
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