Period-index bounds for arithmetic threefolds

The standard period-index conjecture for Brauer groups of p -adic surfaces S predicts that ind ( α ) | per ( α ) 3 for every α ∈ Br ( Q p ( 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 pr...

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Bibliographic Details
Published inInventiones mathematicae Vol. 216; no. 2; pp. 301 - 335
Main Authors Antieau, Benjamin, Auel, Asher, Ingalls, Colin, Krashen, Daniel, Lieblich, Max
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2019
Subjects
Mathematics
Mathematics and Statistics
14F22
16K50
14J20
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Summary:The standard period-index conjecture for Brauer groups of p -adic surfaces S predicts that ind ( α ) | per ( α ) 3 for every α ∈ Br ( Q p ( 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 6 p , giving the first uniform period-index bounds over such fields.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-019-00860-x