Adam Chapman

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20142024

most cited

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-Central Subspaces of Central Simple Algebras

4 citations · 6 across the 12 of their papers we have counts for

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11 papers · 1 filter

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 $v \in V$ …

math.RA2024

Linkage and Essential $p$ -Dimension

Adam Chapman

We prove that two cyclically linked $p$ -algebras of prime degree become inseparably linked under a prime to $p$ extension if and only if the essential $p$ -dimension of the pair is…

math.RA2024

Totally ramified subfields of $p$ -Algebras

Adam Chapman, S. Srimathy

We conjecture that a $p$ -algebra over a complete discrete valued field $K$ contains a totally ramified purely inseparable subfield if and only if it contains a totally ramified cyc…

math.RA2023

Chain Lemma, Quadratic Forms and Symbol Length

Adam Chapman, Ilan Levin

We want to bound the symbol length of classes in $_{2^{m - 1}} B r (F)$ which are represented by tensor products of 5 or 6 cyclic algebras of degree $2^{m}$ . The main ingredients are th…

math.RA2022

Essential Dimension of Central Simple Algebras of Degree 8 and Exponent 2 in Characteristic 2

Adam Chapman

The goal of this note is to reduce the existing upper bound for the essential dimension of central simple algebras of degree 8 and exponent 2 over fields of characteristic 2 from 1…

math.RA2016

Symbol $p$ -Algebras of Prime Degree and their $p$ -Central Subspaces

Adam Chapman, Michael Chapman

We prove that the maximal dimension of a $p$ -central subspace of the generic symbol $p$ -algebra of prime degree $p$ is $p + 1$ . We do it by proving the following number theoretic fac…

Spaces with Vanishing Characteristic Coefficients

Linkage and Essential p-Dimension

Totally ramified subfields of p-Algebras

Chain Lemma, Quadratic Forms and Symbol Length

Essential Dimension of Central Simple Algebras of Degree 8 and Exponent 2 in Characteristic 2

Symbol p-Algebras of Prime Degree and their p-Central Subspaces

Linkage and Essential $p$ -Dimension

Totally ramified subfields of $p$ -Algebras

Symbol $p$ -Algebras of Prime Degree and their $p$ -Central Subspaces