Informatics and Automation, Multidimensional algebraic geometry, Tome 264 (2009), pp. 55-62
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I. V. Dolgachev. On Elements of Order $p^s$ in the Plane Cremona Group over a Field of Characteristic $p$. Informatics and Automation, Multidimensional algebraic geometry, Tome 264 (2009), pp. 55-62. http://geodesic.mathdoc.fr/item/TRSPY_2009_264_a5/
@article{TRSPY_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 = {Informatics and Automation},
pages = {55--62},
year = {2009},
volume = {264},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TRSPY_2009_264_a5/}
}
TY - JOUR
AU - I. V. Dolgachev
TI - On Elements of Order $p^s$ in the Plane Cremona Group over a Field of Characteristic $p$
JO - Informatics and Automation
PY - 2009
SP - 55
EP - 62
VL - 264
UR - http://geodesic.mathdoc.fr/item/TRSPY_2009_264_a5/
LA - en
ID - TRSPY_2009_264_a5
ER -
%0 Journal Article
%A I. V. Dolgachev
%T On Elements of Order $p^s$ in the Plane Cremona Group over a Field of Characteristic $p$
%J Informatics and Automation
%D 2009
%P 55-62
%V 264
%U http://geodesic.mathdoc.fr/item/TRSPY_2009_264_a5/
%G en
%F TRSPY_2009_264_a5
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 $p^2$.
[1] Cossec F. R., Dolgachev I. V., Enriques surfaces, I, Progr. Math., 76, Birkhäuser, Boston, 1989 | MR | Zbl
[2] Demazure M., “Surfaces de Del Pezzo. I–V”, Séminaire sur les singularités des surfaces, Lect. Notes Math., 777, eds. M. Demazure, H. Pinkham, B. Teissier, Springer, Berlin, 1980, 21–69 | DOI | MR
[3] Dolgachev I. V., Iskovskikh V. A., “Finite subgroups of the plane Cremona group”, Algebra, arithmetic and geometry: Manin Festschrift, Progr. Math., 269, 270, Birkhäuser, Boston, 2009 ; arXiv: math.AG/0610595 | Zbl
[4] Silverman J. H., The arithmetic of elliptic curves, Grad. Texts Math., 106, Springer, New York, 1992 | MR