Le groupe de Cremona et ses sous-groupes finis
Séminaire Bourbaki : volume 2008/2009 exposés 997-1011 - Avec table par noms d'auteurs de 1848/49 à 2008/09, Astérisque no. 332  (2010), Talk no. 1000, p. 75-100
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@incollection{AST_2010__332__75_0,
     author = {Serre, Jean-Pierre},
     title = {Le groupe de Cremona et ses sous-groupes finis},
     booktitle = {S\'eminaire Bourbaki : volume 2008/2009 expos\'es 997-1011  - Avec table par noms d'auteurs de 1848/49 \`a 2008/09},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {332},
     year = {2010},
     note = {talk:1000},
     pages = {75-100},
     zbl = {1257.14012},
     mrnumber = {2648675},
     language = {fr},
     url = {http://www.numdam.org/item/AST_2010__332__75_0}
}
Serre, Jean-Pierre. Le groupe de Cremona et ses sous-groupes finis, in Séminaire Bourbaki : volume 2008/2009 exposés 997-1011  - Avec table par noms d'auteurs de 1848/49 à 2008/09, Astérisque, no. 332 (2010), Talk no. 1000, pp. 75-100. http://www.numdam.org/item/AST_2010__332__75_0/

[AW 97] D. Abramovich & J. Wang - Equivariant resolution of singularities in characteristic 0, Math. Res. Lett. 4 (1997), p. 427-433. | Article | MR 1453072 | Zbl 0906.14005

[Be 07] A. Beauville - p-elementary subgroups of the Cremona group, J. Algebra 314 (2007), p. 553-564. | Article | MR 2344578 | Zbl 1126.14017

[BB 04] A. Beauville & J. Blanc - On Cremona transformations of prime order, C. R. Math. Acad. Sci. Paris 339 (2004), p. 257-259. | Article | MR 2092009 | Zbl 1062.14017

[BM 97] E. Bierstone & P. D. Milman - Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Invent, math. 128 (1997), p. 207-302. | Article | MR 1440306 | Zbl 0896.14006

[Bl 06] J. Blanc - Conjugacy classes of affine automorphisms of 𝕂 n and linear automorphisms of n in the Cremona groups, Manuscripta Math. 119 (2006), p. 225-241. | Article | MR 2215969 | Zbl 1093.14017

[Bl 06b] J. Blanc, Finite abelian subgroups of the Cremona group of the plane, Univ. Genève, thèse n° 3777 (2006). | Zbl 1141.14306

J. Blanc, Finite abelian subgroups of the Cremona group of the plane. Voir aussi C. R. Math. Acad. Sci. Paris 344 (2007), p. 21-26. | Article | MR 2286582 | Zbl 1111.14003

[Bl 67] D. M. Bloom - The subgroups of PSL(3,q) for odd q, Trans. Amer. Math. Soc. 127 (1967), p. 150-178. | MR 214671 | Zbl 0153.03702

[BR 97] J. Buhler & Z. Reichstein - On the essential dimension of a finite group, Compositio Math. 106 (1997), p. 159-179. | Article | MR 1457337 | Zbl 0905.12003

[CKM 07] J.-L. Colliot-Thélène, N. A. Karpenko & A. S. Merkur'Ev - Rational surfaces and the canonical dimension of the group PGL 6 , Algebra i Analiz 19 (2007), p. 159-178 (en russe) ; traduction anglaise : St. Petersburg Math. J. 19 (2008), p. 793-804. | MR 2381945 | Zbl 1206.14070

[CO 90] P. Cragnolini & P. A. Oliverio - On the proof of Castelnuovo's rationality criterion in positive characteristic, J. Pure Appl. Algebra 68 (1990), p. 297-323. | Article | MR 1082241 | Zbl 0741.14021

[De 70] M. Demazure - Sous-groupes algébriques de rang maximum du groupe de Cremona, Ann. Sci. École Norm. Sup. 3 (1970), p. 507-588. | Article | Numdam | MR 284446 | Zbl 0223.14009

[De 80] M. Demazure, Surfaces de Del Pezzo, I-IV, in Séminaire sur les Singularités des Surfaces, Lecture Notes in Math., vol. 777, Springer, 1980, p. 21-69. | Article | Numdam | Numdam | Numdam | Numdam | Zbl 0415.00010 | Zbl 0444.14024

[Do 07] I. V. Dolgachev - Topics in classical algebraic geometry, part I, notes de cours, Univ. Michigan, Ann Arbor, 2007.

[Do 08] I. V. Dolgachev, On elements of order p s in the plane Cremona group over a field of characteristic p, à paraître. | Article | Zbl 1312.14044

[DI 07] I. V. Dolgachev & V. A. Iskovskikh - Finite subgroups of the plane Cremona group, in Algebra, Arithmetic and Geometry, Manin's Festschrift, Progress in Math., vol. 269, Birkhäuser, 2008. | MR 2641179 | Zbl 1219.14015

[DI 08] I. V. Dolgachev & V. A. Iskovskikh, On elements of prime order in the plane Cremona group over a perfect field, prépublication arXiv:0707.4305. | Article | MR 2535007 | Zbl 1188.14007

[Fo 73] J. Fogarty - Fixed point schemes, Amer. J. Math. 95 (1973), p. 35-51. | Article | MR 332805 | Zbl 0272.14012

[Fr 11] F. G. Frobenius - Über den von L. Bieberbach gefundenen Beweis eines Satzes von C. Jordan, Sitz. Kön. Preuss. Akad. Berlin (1911), p. 241-248 (= Ges. Abh., vol. III, 493-500). | JFM 42.0152.01

[Gr 59] A. Grothendieck - Géométrie formelle et géométrie algébrique, Séminaire Bourbaki, vol. 1958/59, exposé n° 182, Astérisque (hors série) 5 (1995), p. 193-220 ; erratum p. 390. | Numdam | MR 1603467 | Zbl 0229.14005

[Ha 77] R. Hartshorne - Algebraic geometry, Springer, 1977, Graduate Texts in Mathematics, No. 52. | Article | MR 463157 | Zbl 0367.14001

[Il 77] L. Illusie - Formule de Lefschetz pour les faisceaux cohérents, in Cohomologie l-adique et fonctions L (SGA 5), Lecture Notes in Math., Springer, 1977, p. 73-137.

[Il 05] L. Illusie, Grothendieck's existence theorem in formal geometry, in Fundamental algebraic geometry, Math. Surveys Monogr., vol. 123, Amer. Math. Soc., 2005, p. 179-233. | MR 2223409 | Zbl 1085.14001

[Is 79] V. A. Iskovskikh - Modèles minimaux de surfaces rationnelles sur des corps quelconques (en russe), Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), p. 19-43 ; traduction anglaise : Math. USSR Izvestija 14 (1980), p. 17-39. | Zbl 0427.14011

[Is 96] V. A. Iskovskikh, Factorisation des applications birationnelles de surfaces rationnelles du point de vue de la théorie de Mori (en russe), Uspekhi Math. Nauk 51 (1996), p. 3-72 ; traduction anglaise : Russian Math. Surveys 51 (1996), p. 585-652. | Zbl 0914.14005

[Iv 72] B. Iversen - A fixed point formula for action of tori on algebraic varieties, Invent. math. 16 (1972), p. 229-236. | Article | MR 299608 | Zbl 0246.14010

[Ko 96] J. Kollár - Rational curves on algebraic varieties, Ergebnisse Math. Grenzg., vol. 32, Springer, 1996. | MR 1440180 | Zbl 0877.14012

[Ko 07] J. Kollár, Lectures on resolution of singularities, Annals of Math. Studies, vol. 166, Princeton Univ. Press, 2007. | MR 2289519 | Zbl 1113.14013

[KS 00] J. Kollár & E. Szabó - Fixed points of group actions and rational maps, Canadian J. Math. 52 (2000), p. 1054-1056. | MR 1782331

[Ma 66] Y. I. Manin - Les surfaces rationnelles sur les corps parfaits, Publ. Math. IHÉS 30 (1966), p. 415-475.

[Ma 67] Y. I. Manin, Les surfaces rationnelles sur les corps parfaits (en russe) II, Mat. Sbornik 72 (1967), p. 161-192 ; traduction anglaise : Math. USSR Sbornik 1 (1967), p. 141-168. | Zbl 0182.23701

[Ma 86] Y. I. Manin, Cubic forms, 2e éd., North-Holland Mathematical Library, vol. 4, North-Holland Publishing Co., 1986. | MR 833513 | Zbl 0582.14010

[Mi 87] H. Minkowski - Zur Theorie der positiven quadratischen Formen, J. Crelle 101 (1887), p. 196-202 (= Ges. Abh., Band I, n° VI). | JFM 19.0189.01 | MR 1580123

[Mi 11] H. H. Mitchell - Determination of the ordinary and modular ternary linear groups, Trans. Amer. Math. Soc. 12 (1911), p. 207-242. | Article | JFM 42.0161.01 | MR 1500887

[Mo 82] S. Mori - Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982), p. 133-176. | Article | MR 662120 | Zbl 0557.14021

[RY 00] Z. Reichstein & B. Youssin - Essential dimensions of algebraic groups and a resolution theorem for G-varieties, Canad. J. Math. 52 (2000), p. 1018-1056. | Article | MR 1782331 | Zbl 1044.14023

[RY 02] Z. Reichstein & B. Youssin, A birational invariant for algebraic group actions, Pacific J. Math. 204 (2002), p. 223-246. | Article | MR 1905199 | Zbl 1054.14062

[Se 99] J-P. Serre - Sous-groupes finis des groupes de Lie, Séminaire Bourbaki, vol. 1998/99, exposé n° 864, Astérisque 266 (2000), p. 415-430. | Numdam | MR 1772682 | Zbl 0968.20025

[Se 03] J-P. Serre, Cohomological invariants, Witt invariants, and trace forms (Notes by Skip Garibaldi), in Cohomological invariants in Galois cohomology, Univ. Lecture Ser., vol. 28, Amer. Math. Soc., 2003, p. 1-100. | MR 1999384

[Se 07] J-P. Serre, Bounds for the orders of the finite subgroups of G(k), in Group representation theory, EPFL Press, Lausanne, 2007, p. 405-450. | MR 2336645 | Zbl 1160.20043

[Se 08] J-P. Serre, How to use finite fields for problems concerning infinite fields, à paraître dans Contemp. Math. 487, AMS, p. 183-193. | Article | MR 2555994 | Zbl 1199.14007

[Se 09] J-P. Serre, A Minkowski-style bound for the orders of the finite subgroups of the Cremona group of rank 2 over an arbitrary field, Moscow Math. J. 9 (2009), p. 193-208. | MR 2567402

[Sk 01] A. Skorobogatov - Torsors and rational points, Cambridge Tracts in Mathematics, vol. 144, Cambridge Univ. Press, 2001. | MR 1845760 | Zbl 0972.14015

[Vo 98] V. E. Voskresenskiĭ - Algebraic groups and their birational invariants, Translations of Mathematical Monographs, vol. 179, Amer. Math. Soc., 1998. | MR 1634406 | Zbl 0974.14034

[Zh 01] D.-Q. Zhang - Automorphisms of finite order on rational surfaces, J. Algebra 238 (2001), p. 560-589. | Article | MR 1823774 | Zbl 1057.14053