On Elements of Prime Order in the Plane Cremona Group over a Perfect Field

Abstract

We show that the plane Cremona group over a perfect field k of characteristic p ≥ 0 contains an element of prime order l ≥ 7 not equal to p if and only if there exists a two-dimensional algebraic torus T over k such that T(k) contains an element of order l. If p = 0 and k does not contain a primitive lth root of unity, we show that there are no elements of prime order l > 7 in and all elements of order 7 are conjugate.