Essential dimension of generic symbols in characteristic p

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Abstract

In this article the -essential dimension of generic symbols over fields of characteristic is studied. In particular, the -essential dimension of the length generic -symbol of degree is bounded below by when the base field is algebraically closed of characteristic . The proof uses new techniques for working with residues in Milne-Kato -cohomology and builds on work of Babic and Chernousov in the Witt group in characteristic 2. Two corollaries on -symbol algebras (i.e, degree 2 symbols) result from this work. The generic -symbol algebra of length is shown to have -essential dimension equal to as a -torsion Brauer class. The second is a lower bound of on the -essential dimension of the functor . Roughly speaking this says that you will need at least independent parameters to be able to specify any given algebra of degree and exponent over a field of characteristic and improves on the previously established lower bound of 3.

Original languageEnglish
JournalForum of Mathematics, Sigma
Volume5
DOIs
StatePublished - 2017

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