Geodesic
On Elements of Order $p^s$ in the Plane Cremona Group over a~Field of Characteristic~$p$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Multidimensional algebraic geometry, Tome 264 (2009), pp. 55-62

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We show that the plane Cremona group over a field of characteristic $p>0$ does not contain elements of order of power of $p$ larger than $2$. We also describe conjugacy classes of elements of order $p^2$. 
@article{TM_2009_264_a5,
     author = {I. V. Dolgachev},
     title = {On {Elements} of {Order} $p^s$ in the {Plane} {Cremona} {Group} over {a~Field} of {Characteristic~}$p$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {55--62},
     publisher = {mathdoc},
     volume = {264},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_264_a5/}
}
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I. V. Dolgachev. On Elements of Order $p^s$ in the Plane Cremona Group over a~Field of Characteristic~$p$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Multidimensional algebraic geometry, Tome 264 (2009), pp. 55-62. http://geodesic.mathdoc.fr/item/TM_2009_264_a5/