@inproceedings{0292d3766edc405789d638ac9a98fc18,

title = "Asymptotic Brauer p-dimension",

abstract = "We deﬁne and compute the asymptotic Brauer p-dimension of a ﬁeld F, denoted ABrdp(F), in cases where F is a rational function ﬁeld or Laurent series ﬁeld. ABrdp(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 F0(α1,…, αn) and F0((α1))… ((αn)) where F0 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 = F0((α1))… ((αn)) and F0 is algebraically closed of characteristic not p.",

keywords = "Division algebras, cyclic algebras, fields of positive characteristic, linkage, valuation theory",

author = "Adam Chapman and Kelly McKinnie",

note = "Publisher Copyright: {\textcopyright} 2023 American Mathematical Society.; Virtual Conference in Honor of Tariq Rizvi Noncommutative Rings and their Application VII, NCRA 2021, and Virtual Conference on Quadratic forms, rings and codes, QFRC 2021 ; Conference date: 08-07-2021 Through 08-07-2021",

year = "2023",

doi = "10.1090/conm/785/15775",

language = "English",

isbn = "9781470468590",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "57--66",

editor = "A. Leroy and S.K. Jain",

booktitle = "Algebra and Coding Theory- Virtual Conference in Honor of Tariq Rizvi Noncommutative Rings and their Applications VII, 2021 and Virtual Conference on Quadratic Forms, Rings and Codes, 2021",

}