The standard period-index conjecture for Brauer groups of p-adic surfaces S predicts that ind(α)|per(α)3 for every α∈Br(Qp(S)). Using Gabber’s theory of prime-to-ℓ alterations and the deformation theory of twisted sheaves, we prove that ind(α)|per(α)4 for α of period prime to 6p, giving the first uniform period-index bounds over such fields.
Inventiones Mathematicae
School of Mathematics and Statistics

Antieau, B. (Benjamin), Auel, A. (Asher), Ingalls, C, Krashen, D. (Daniel), & Lieblich, M. (Max). (2019). Period-index bounds for arithmetic threefolds. Inventiones Mathematicae. doi:10.1007/s00222-019-00860-x