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Period-index bounds for arithmetic threefolds (1704.05489v3)
Published 18 Apr 2017 in math.AG and math.RA
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.