Is there a classification of quadric hypersurfaces $Q\subset \mathbb{P}^r$ over an algebraically closed field of characteristic 2?
Quadrics in characteristic 2
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algebraic-geometry
reference-request
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2Any such quadric is of the form $\sum x_iy_i$ or $\sum x_iy_i+z^2$., where $x_i, y_i, z$ are variables. – 2017-01-31
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0Is the content of your statement that I can make all the coefficients 0 or 1, or is there also a restriction on which monomials can appear? – 2017-02-06
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0What exactly do you mean `can make'? After a (linear) change of variables, you can assume what I said. Of course all variables (of $r$-space) may not appear. – 2017-02-06
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0I just mean a linear change of variables. For example, suppose we are working in $\overline{\mathbb{F}_2}$ and $a$ is the generator of $\mathbb{F}_4$ over $\mathbb{F}_2$. If I have the quadratic form $x^2+xy+ay^2$, what linear change of variables do I choose? – 2017-02-06
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0Oh, I see, we can replace $x$ by $x+(1-a)y$... – 2017-02-06
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0@Mohan, do you have a textbook reference for that? – 2018-03-02