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Generalized Brauer dimension of semi-global fields
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Gosavi, Saurabh. Generalized Brauer dimension of semi-global fields. Retrieved from https://doi.org/doi:10.7282/t3-3v35-h066

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TitleGeneralized Brauer dimension of semi-global fields
NameGosavi, Saurabh (author); Krashen, Daniel (chair); Carbone, Lisa (internal member); Weibel, Charles A. (internal member); Harbater, David (outside member); Rutgers University; School of Graduate Studies
Date Created2020
Other Date2020-10 (degree)
SubjectBrauer group, Mathematics
Extent1 online resource (vii, 123 pages)
DescriptionLet $F$ be a one variable function field over a complete discretely valued field with residue field $k$. Let $n$ be a positive integer, coprime to the characteristic of $k$. Given a finite subgroup $B$ in the $n$-torsion part of the Brauer group ${}_{n}br(F)$, we define the index of $B$ to be the minimum of the degrees of field extensions which split all elements in $B$. In this thesis, we improve an upper bound for the index of $B$, given by Parimala-Suresh, in terms of arithmetic invariants of $k$ and $k(t)$. As a simple application of our result, given a quadratic form $q/F$, where $F$ is a function field in one variable over an $m$-local field, we provide an upper-bound to the minimum of degrees of field extensions $L/F$ so that the Witt index of $q otimes L$ becomes the largest possible.
NotePh.D.
NoteIncludes bibliographical references
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/t3-3v35-h066
LanguageEnglish
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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