18 citations · 29 across the 15 of their papers we have counts for
15 papers · 1 filter
The -Invariant of Fields of Characteristic 2
Adam Chapman, Kelly McKinnie
We study the minimal dimension of a nonsingular anisotropic universal quadratic form over a field of , which we call the ``-invariant" of . We s…
Essential Dimension of Central Simple Algebras when the Characteristic is Bad
Adam Chapman, Kelly McKinnie
This is a survey of the existing literature, the state of the art, and a few minor new results and open questions regarding the essential dimension of central simple algebras and f…
Classes in of lower exponent
Adam Chapman, Daniel Krashen, Kelly McKinnie
Let be a field of characteristic . We prove that if a symbol in is of exponent dividing , then its s…
Biquaternion Algebras, Chain Lemma and Symbol Length
Adam Chapman, Kelly McKinnie
In this note, we present a chain lemma for biquaternion algebras over fields of characteristic 2 in the style of the equivalent chain lemma by Sivatski in characteristic not 2, and…
Asymptotic Brauer -Dimension
Adam Chapman, Kelly McKinnie
We define and compute , the asymptotic Brauer -dimension of a field , in cases where is a rational function field or Laurent series field. $\ope…
Common Splitting Fields of Symbol Algebras
Adam Chapman, Mathieu Florence, Kelly McKinnie
We study the common splitting fields of symbol algebras of degree over fields of . We first show that if any finite number of such algebras shar…
Essential Dimension, Symbol Length and -rank
Adam Chapman, Kelly McKinnie
We prove that the essential dimension of central simple algebras of degree and exponent over fields containing a base-field of characteristic is at l…
Essential Dimension of Generic Symbols in Characteristic p
Kelly McKinnie
In this article the -essential dimension of generic symbols over fields of characteristic is studied. In particular, the -essential dimension of the length generic…
Kato-Milne Cohomology and Polynomial Forms
Adam Chapman, Kelly McKinnie
Given a prime number , a field with and a positive integer , we study the class-preserving modifications of Kato-Milne classes of decomposable…
Cyclic Length in the Tame Brauer Group of the Function Field of a p-Adic Curve
Eric Brussel, Kelly McKinnie, Eduardo Tengan
Let be the function field of a smooth curve over the -adic number field $\Q_p$. We show that for each prime-to- number the -torsion subgroup $\H^2(F,μ_n)={}_n\Br(F…
Distinguishing division algebras by finite splitting fields
Daniel Krashen, Kelly McKinnie
This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to de…
Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves
Eric Brussel, Kelly McKinnie, Eduardo Tengan
We construct indecomposable and noncrossed product division algebras over function fields of smooth curves X over Z_p. This is done by defining an index preserving morphism s:Br(\h…
Degeneracy and decomposability in abelian crossed products
Kelly McKinnie
In this paper we study the relationship between degeneracy and decomposability in abelian crossed products. In particular we construct an indecomposable abelian crossed product div…
Indecomposable p-algebras and Galois subfields in generic abelian crossed products
Kelly McKinnie
Let F be a Henselian valued field with char(F) = p and D a semi-ramified, "not strongly degenerate" p-algebra. We show that all Galois subfields of D are inertial. Using this as a…
Prime to p extensions of the generic abelian crossed product
Kelly McKinnie
We prove that the noncyclic generic abelian crossed product p-algebras constructed by Amitsur and Saltman remain noncyclic after tensoring by any prime to p extension.