Questions tagged [characteristic-2]

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Is there any point in considering Form Rings when 2 admits an inverse?

In the study of quadratic spaces over general rings, there is a type of scalar which people consider called a Form ring $(R,\Lambda)$ relative to some anti-automorphism denoted $(-)^J:R\to R$ and ...
• 4,863
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Proof of Theorem Concerning Conway's "Nim Field"

I have a question about the proof of theorem 44 in "On Numbers and Games" on page 58, concerning the "Nim field" ${ON}_2$. As background, ${ON}_2$ turns the ordinals into a field ...
• 449
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Solving efficiently a quadratic equation in a large finite field of characteristic two

I'm trying to solve efficiently a quadratic equation in the finite field $\text{GF}(2^{128})$ represented as $(\mathbb{Z}/2\mathbb{Z})[x] / (x^{128} + x^7 + x^2 + x + 1)$. Until now, I came across ...
• 21
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Generators of the orthogonal group of a quadratic form in odd dimension in characteristic 2

In characteristic not $2$, the Theorem of Cartan-Dieudonné states: [Grove, Theorem 6.6]: Let $q$ be a nondegenerate symmetric quadratic form of dimension $n$ in characteristic not $2$. Then every ...
• 168
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Surfaces of general type with $h^1(-K_X)\neq 0$

By a result of Ekedahl, in characteristic 2 one may have minimal surfaces of general type such that $h^1(X,-K_X)\neq 0$ and $X$ is birational to an inseparable double cover of a rational surface. How ...
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