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Dissertation/Thesis Abstract

Generalized Brauer Dimension of Semi-Global Fields
by Gosavi, Saurabh, Ph.D., Rutgers The State University of New Jersey, School of Graduate Studies, 2020, 131; 27956983
Abstract (Summary)

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 nBr(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 qL becomes the largest possible.

Indexing (document details)
Advisor: Krashen, Daniel
Commitee: Harbater, David, Carbone, Lisa, Weibel, Charles A.
School: Rutgers The State University of New Jersey, School of Graduate Studies
Department: Mathematics
School Location: United States -- New Jersey
Source: DAI-B 82/7(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Brauer group, Generalized Brauer Dimension, Period-index problem, Quadratic forms, Semi-global fields
Publication Number: 27956983
ISBN: 9798557093026
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