Adam Chapman

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20152023

most citedRoots and Critical Points of Polynomials over Cayley--Dickson Algebras

2 citations · 2 across the 4 of their papers we have counts for

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math.AC2019

Linkage of sets of Quaternion Algebras in characteristic 2

Adam Chapman

This note contains two new observations on the linkage properties of quaternion algebras over fields of characteristic 2: first, that a 3-linked field need not be 4-linked (a case…

math.AC2019

Linkage of Pfister forms over $C (x_{1}, \dots, x_{n})$

Adam Chapman, Jean-Pierre Tignol

In this note, we prove the existence of a set of $n$ -fold Pfister forms of cardinality $2^{n}$ over $C (x_{1}, \dots, x_{n})$ which do not share a common $(n - 1)$ -fold factor. This…

math.AC2018

The descent of biquaternion algebras in characteristic two

Demba Barry, Adam Chapman, Ahmed Laghribi

In this paper we associate an invariant to a biquaternion algebra $B$ over a field $K$ with a subfield $F$ such that $K / F$ is a quadratic separable extension and $\operatorname{cha…

math.AC2018

Types of Linkage of Quadratic Pfister Forms

Adam Chapman, Andrew Dolphin

Given a field $F$ of positive characteristic $p$ , $θ \in H_{p}^{n - 1} (F)$ and $β, γ \in F^{\times}$ , we prove that if the symbols $θ \land \frac{d β}{β}$ and $θ \land \frac{d γ}{γ}$ in $H_p^n(…

math.AC2017

The $u^{n}$ -invariant and the Symbol Length of $H_{2}^{n} (F)$

Adam Chapman, Kelly McKinnie

Given a field $F$ of $char (F) = 2$ , we define $u^{n} (F)$ to be the maximal dimension of an anisotropic form in $I_{q}^{n} F$ . For $n = 1$ it recaptures the definition of $u(F)…

Linkage of sets of Quaternion Algebras in characteristic 2

Linkage of Pfister forms over C(x1​,…,xn​)

The descent of biquaternion algebras in characteristic two

Types of Linkage of Quadratic Pfister Forms

The un-invariant and the Symbol Length of H2n​(F)

Linkage of Pfister forms over $C (x_{1}, \dots, x_{n})$

The $u^{n}$ -invariant and the Symbol Length of $H_{2}^{n} (F)$