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On Brauer p-dimensions and index-exponent relations over finitely-generated field extensions

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Let E be a field of absolute Brauer dimension abrd(E), and F/E a transcendental finitely-generated extension. This paper shows that the Brauer dimension Brd(F) is infinite, if abrd\({(E) = \infty }\) . When the absolute Brauer p-dimension abrd p (E) is infinite, for some prime number p, it proves that for each pair (n, m) of integers with \({n \ge m > 0}\), there is a central division F-algebra of Schur index p n and exponent p m. Lower bounds on the Brauer p-dimension Brd p (F) are obtained in some important special cases where abrd p \({(E) < \infty }\) . These results solve negatively a problem posed by Auel et al. (Transf. Groups 16:219–264, 2011).

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 8, 1113, Sofia, Bulgaria

    I. D. Chipchakov

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  1. I. D. Chipchakov
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Correspondence to I. D. Chipchakov.

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Throughout this paper, we write for brevity “FG-extension(s)” instead of “finitely-generated [field] extension(s)”.

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Chipchakov, I.D. On Brauer p-dimensions and index-exponent relations over finitely-generated field extensions. manuscripta math. 148, 485–500 (2015). https://doi.org/10.1007/s00229-015-0745-7

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