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 language | English |
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| Journal | Forum of Mathematics, Sigma |
| Volume | 5 |
| DOIs | |
| State | Published - 2017 |
Funding
The author would like to thank Skip Garibaldi for introducing the problem. He also thanks Parimala and Suresh Venapally at Emory University, for their helpful comments, time and support during a visit. The author would also like to thank Stephan Tillmann (ARC Discovery Grant DP140100158) at the University of Sydney for support during the writing of this paper.
| Funders | Funder number |
|---|---|
| Emory University | |
| Western Sydney University |