Adam Chapman

collaborators

4 papers

math.RA2026

The $m$ -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 $F$ of $char (F) = 2$ , which we call the `` $m$ -invariant" of $F$ . We s…

math.KT2026

Sums of two symbols in $K_{2} (F) /2 K_{2} (F)$ in characteristic two

Demba Barry, Adam Chapman, Ahmed Laghribi

In this paper, study sums $A = {a, b}_{2} + {c, d}_{2}$ of two symbols in $K_{2} (F) /2 K_{2} (F)$ when $char (F) = 2$ . We first prove a chain lemma that connects $A$ to $B=\{α,β\}_2…

math.RA2024

Classes in $H_{p^{m}}^{n + 1} (F)$ of lower exponent

Adam Chapman, Daniel Krashen, Kelly McKinnie

Let $F$ be a field of characteristic $p > 0$ . We prove that if a symbol $A = ω \otimes β_{1} \otimes \dots \otimes β_{n}$ in $H_{p^{m}}^{n + 1} (F)$ is of exponent dividing $p^{m - 1}$ , then its s…

math.RA2024

Spaces with Vanishing Characteristic Coefficients

Adam Chapman

We prove that the maximal dimension of a subspace $V$ of the generic tensor product of $m$ symbol algebras of prime degree $p$ with $Tr (v^{p - 1}) = 0$ for all $v \in V$ …

The m-Invariant of Fields of Characteristic 2

Sums of two symbols in K2​(F)/2K2​(F) in characteristic two

Classes in Hpmn+1​(F) of lower exponent

Spaces with Vanishing Characteristic Coefficients

The $m$ -Invariant of Fields of Characteristic 2

Sums of two symbols in $K_{2} (F) /2 K_{2} (F)$ in characteristic two

Classes in $H_{p^{m}}^{n + 1} (F)$ of lower exponent