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Zev Rosengarten and I have written up a self-contained proof of this fact. It is available on Thuses. The proof is entirely algebraic, works over any separably closed field of $\text{char} \neq 2$, and does not use any Hodge theory.

Zev Rosengarten and I have written up a self-contained proof of this fact. It is available on Thuses. The proof is entirely algebraic, works over any separably closed field of $\text{char} \neq 2$, and does not use any Hodge theory.

I have written up a self-contained proof of this fact. It is available on Thuses. The proof is entirely algebraic, works over any separably closed field of $\text{char} \neq 2$, and does not use any Hodge theory.

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Zev Rosengarten and I have written up a self-contained proof of this fact. It is available on my website hereThuses. The proof is entirely algebraic, works over any separably closed field of $\text{char} \neq 2$, and does not use any Hodge theory.

Zev Rosengarten and I have written up a self-contained proof of this fact. It is available on my website here. The proof is entirely algebraic, works over any separably closed field of $\text{char} \neq 2$, and does not use any Hodge theory.

Zev Rosengarten and I have written up a self-contained proof of this fact. It is available on Thuses. The proof is entirely algebraic, works over any separably closed field of $\text{char} \neq 2$, and does not use any Hodge theory.

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Zev Rosengarten and I have written up a self-contained proof of this fact. It is available on my website herehere. The proof is entirely algebraic, works over any separably closed field of $\text{char} \neq 2$, and does not use any Hodge theory.

Zev Rosengarten and I have written up a self-contained proof of this fact. It is available on my website here. The proof is entirely algebraic, works over any separably closed field of $\text{char} \neq 2$, and does not use any Hodge theory.

Zev Rosengarten and I have written up a self-contained proof of this fact. It is available on my website here. The proof is entirely algebraic, works over any separably closed field of $\text{char} \neq 2$, and does not use any Hodge theory.

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