Nicolas Grenier-Boley: On the triviality of certain Whitehead groups

Submission: 2006, Mar 15

Let K be a field of arbitrary characteristic and q be a prime number different from the characteristic of K. If A is a central simple algebra over K whose index is a power of q, we show the triviality of the reduced Whitehead group and of the reduced unitary Whitehead group when the cohomological q-dimension of K is at most 2. We give a global version of this result and indicate what can be done in the case where the index of the algebra is a power of the characteristic of the field.

2000 Mathematics Subject Classification: 19Bxx

Keywords and Phrases: Central simple algebra, Whitehead group

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