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Abstract: We show that the plane Cremona group over a perfect field $k$ ofcharacteristic $p \ge 0$ contains an element of prime order $\ell\ge 7$ notequal to $p$ if and only if there exists a 2-dimensional algebraic torus $T$over $k$ such that $Tk$ contains an element of order $\ell$. If $p = 0$ and$k$ does not contain a primitive $\ell$-th root of unity, we show that thereare no elements of prime order $\ell > 7$ in $\Cr 2k$ and all elements oforder 7 are conjugate.



Author: Igor V. Dolgachev, Vasily A. Iskovskikh

Source: https://arxiv.org/







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