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Un Invariant De Degre 3 Des Algebres Centrales Simples D’exposant 2


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1 Institut De Mathematiques De Jussieu, UPMC-UFR 929, Mathematiques, 4 Place Jussieu-75005, Paris, France
     

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We associate to any central simple algebra A of exponent 2 over a field of characteristic ≠2 an invariant with values in the degree 3 unramified cohomology of its Severi-Brauer variety modulo the image of the cohomology of the ground field. The main theorem is that this invariant is nonzero if and only if the index of A is ≥8.
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  • Un Invariant De Degre 3 Des Algebres Centrales Simples D’exposant 2

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Authors

Bruno Kahn
Institut De Mathematiques De Jussieu, UPMC-UFR 929, Mathematiques, 4 Place Jussieu-75005, Paris, France

Abstract


We associate to any central simple algebra A of exponent 2 over a field of characteristic ≠2 an invariant with values in the degree 3 unramified cohomology of its Severi-Brauer variety modulo the image of the cohomology of the ground field. The main theorem is that this invariant is nonzero if and only if the index of A is ≥8.