Adam Chapman

activity

20112024

most citedA Simple Motivated Completion of the Standard Model below the Planck Scale: Axions and Right-Handed Neutrinos

78 citations · 165 across the 30 of their papers we have counts for

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Showing 2017Show all

5 papers · 1 filter

math.AC2017

Common Slots of Bilinear and Quadratic Pfister Forms

Adam Chapman

We show that over any field $F$ of $char (F) = 2$ and 2-rank $n$ , there exist $2^{n}$ bilinear $n$ -fold Pfister forms that have no slot in common. This answers a question…

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)…

math.RA2017

Triple Linkage of Quadratic Pfister Forms

Adam Chapman, Andrew Dolphin, David B. Leep

Given a field $F$ of characteristic 2, we prove that if every three quadratic $n$ -fold Pfister forms have a common quadratic $(n - 1)$ -fold Pfister factor then $I_{q}^{n + 1} F = 0$ . As a…

math.RA2017

Kato-Milne Cohomology and Polynomial Forms

Adam Chapman, Kelly McKinnie

Given a prime number $p$ , a field $F$ with $char (F) = p$ and a positive integer $n$ , we study the class-preserving modifications of Kato-Milne classes of decomposable…

math.RA2017

Differential Forms, Linked Fields and the $u$ -Invariant

Adam Chapman, Andrew Dolphin

We associate an Albert form to any pair of cyclic algebras of prime degree $p$ over a field $F$ with $char (F) = p$ which coincides with the classical Albert form when…

Common Slots of Bilinear and Quadratic Pfister Forms

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

Triple Linkage of Quadratic Pfister Forms

Kato-Milne Cohomology and Polynomial Forms

Differential Forms, Linked Fields and the u-Invariant

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

Differential Forms, Linked Fields and the $u$ -Invariant