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arXiv · 1704.05489

Period-index bounds for arithmetic threefolds

Benjamin Antieau·Asher Auel·Colin Ingalls·Daniel Krashen·Max Lieblich
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Abstract

The standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over a $p$-adic field predicts that the index divides the cube of the period. Using Gabber's theory of prime-to-$\ell$ alterations and the deformation theory of twisted sheaves, we prove that the index divides the fourth power of the period for every Brauer class whose period is prime to $6p$, giving the first uniform period-index bounds over such fields.

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Benjamin Antieau, Asher Auel, Colin Ingalls, Daniel Krashen, Max Lieblich. 2017-04-18. Period-index bounds for arithmetic threefolds. https://doi.org/10.1007/s00222-019-00860-x

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