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 q ⊗ L becomes the largest possible.
|Commitee:||Harbater, David, Carbone, Lisa, Weibel, Charles A.|
|School:||Rutgers The State University of New Jersey, School of Graduate Studies|
|School Location:||United States -- New Jersey|
|Source:||DAI-B 82/7(E), Dissertation Abstracts International|
|Keywords:||Brauer group, Generalized Brauer Dimension, Period-index problem, Quadratic forms, Semi-global fields|
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