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Quadratic Forms, Linear Algebraic Groups, and Cohomology pp 137–171Cite as

Cohomological Invariants of Central Simple Algebras with Involution

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Part of the book series: Developments in Mathematics ((DEVM,volume 18))

Summary

This survey reviews the various invariants with values in Galois cohomology groups that have been defined for involutions on central simple algebras following the model of the discriminant, Clifford invariant, and Arason invariant of quadratic forms. From the orthogonal case to the unitary case to the symplectic case, the degree of the invariants increases but their properties are similar.

To Parimala, with gratitude and admiration

2010 Mathematics subject classification. 11E72.

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Authors and Affiliations

  1. Département de mathématique, Université catholique de Louvain, Chemin du cyclotron, 2, B-1348, Louvain-la-Neuve, Belgium

    Jean-Pierre Tignol

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  1. Jean-Pierre Tignol
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Correspondence to Jean-Pierre Tignol .

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Editors and Affiliations

  1. CNRS, Labo. Mathématiques, Université Paris-Sud XI, Orsay CX, 91405, France

    Jean-Louis Colliot-Thélène

  2. Dept. Mathematics &, Computer Science, Emory University, Dowman Dr. 400, Atlanta, 30322, USA

    Skip Garibaldi

  3. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Rd., Mumbai, 400005, India

    R. Sujatha

  4. Dept. Mathematics & Statistics, University of Hyderabad, Hyderabad, 500046, India

    Venapally Suresh

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Tignol, JP. (2010). Cohomological Invariants of Central Simple Algebras with Involution. In: Colliot-Thélène, JL., Garibaldi, S., Sujatha, R., Suresh, V. (eds) Quadratic Forms, Linear Algebraic Groups, and Cohomology. Developments in Mathematics, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6211-9_8

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