Nous montrons que toute bijection de , pour K un corps fini de caractéristique impaire, est induite par une transformation birationnelle sans point d'indétermination rationnel.
We prove that every permutation of , where K is a finite field with odd characteristic, is induced by a birational transformation with no rational indeterminacy point.
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@article{CRMATH_2009__347_21-22_1289_0, author = {Cantat, Serge}, title = {Birational permutations}, journal = {Comptes Rendus. Math\'ematique}, pages = {1289--1294}, publisher = {Elsevier}, volume = {347}, number = {21-22}, year = {2009}, doi = {10.1016/j.crma.2009.09.019}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2009.09.019/} }
TY - JOUR AU - Cantat, Serge TI - Birational permutations JO - Comptes Rendus. Mathématique PY - 2009 SP - 1289 EP - 1294 VL - 347 IS - 21-22 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2009.09.019/ DO - 10.1016/j.crma.2009.09.019 LA - en ID - CRMATH_2009__347_21-22_1289_0 ER -
Cantat, Serge. Birational permutations. Comptes Rendus. Mathématique, Tome 347 (2009) no. 21-22, pp. 1289-1294. doi : 10.1016/j.crma.2009.09.019. http://archive.numdam.org/articles/10.1016/j.crma.2009.09.019/
[1] On groups containing the projective special linear group, Arch. Math. (Basel), Volume 37 (1981) no. 4, pp. 295-299
[2] Rational real algebraic models of topological surfaces, Doc. Math., Volume 12 (2007), pp. 549-567
[3] Random matrix theory over finite fields, Bull. Amer. Math. Soc. (N.S.), Volume 39 (2002) no. 1, pp. 51-85 (electronic)
[4] Johannes Huisman, Frédéric Mangolte, The group of automorphisms of a real rational surface is n-transitive, preprint, 2008, pp. 1–7
[5] Janos Kollár, Frédéric Mangolte, Cremona transformations and diffeomorphisms of surfaces, preprint, 2008, pp. 1–17
[6] On permutation groups containing as a subgroup, Geom. Dedicata, Volume 4 (1975) no. 2/3/4, pp. 373-375
[7] The structure of Lie algebras of spherical vector fields and the diffeomorphism groups of and , Sibirsk. Mat. Zh., Volume 18 (1977) no. 1, pp. 161-173 (239)
[8] Polynomial automorphisms over finite fields, Serdica Math. J., Volume 27 (2001) no. 4, pp. 343-350
[9] Finite Fields and Applications, Student Mathematical Library, vol. 41, American Mathematical Society, Providence, RI, 2007
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