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arXiv · 2111.15251

Minimal quadratic forms for the function field of a conic in characteristic $2$

Adam Chapman·Anne Quéguiner-Mathieu
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Abstract

In this note, we construct explicit examples of $F_Q$-minimal quadratic forms of dimension $5$ and $7$, where $F_Q$ is the function field of a conic over a field $F$ of characteristic $2$. The construction uses the fact that any set of $n$ cyclic $p$ algebras over a field of characteristic $p$ can be described using only $n+1$ elements of the base field. It also uses a general result that provides an upper bound on the Witt index of an orthogonal sum of two regular anisotropic quadratic forms over a henselian valued field.

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Adam Chapman, Anne Quéguiner-Mathieu. 2021-11-30. Minimal quadratic forms for the function field of a conic in characteristic $2$. https://arxiv.org/abs/2111.15251

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