LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Abstract (type = abstract)
Let $F$ 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.
Subject (authority = local)
Topic
Brauer group
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_10826
PhysicalDescription
Form (authority = gmd)
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (vii, 123 pages)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
RelatedItem (type = host)
TitleInfo
Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier (type = local)
rucore10001600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
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