2021
DOI: 10.48550/arxiv.2109.11918
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Asymptotic Brauer $p$-Dimension

Abstract: We define and compute ABrd p (F), the asymptotic Brauer p-dimension of a field F, in cases where F is a rational function field or Laurent series field. ABrd p (F) is defined like the Brauer p-dimension except it considers finite sets of Brauer classes instead of single classes. Our main result shows that for fields F 0 (α 1 , . . . , α n ) and F 0 ((α 1 )) . . . ((α n )) where F 0 is a perfect field of characteristic p > 0 when n 2 the asymptotic Brauer p-dimension is n. We also show that it is n − 1 when F =… Show more

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