On the deformation of Artin-Schreier to Kummer
Sekiguchi, T. ; Oort, F. ; Suwa, N.
Annales scientifiques de l'École Normale Supérieure, Tome 22 (1989), p. 345-375 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_1989_4_22_3_345_0,
     author = {Sekiguchi, Takesi and Oort, Frans and Suwa, Noriyuki},
     title = {On the deformation of Artin-Schreier to Kummer},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {22},
     year = {1989},
     pages = {345-375},
     doi = {10.24033/asens.1586},
     mrnumber = {91g:14041},
     zbl = {0714.14024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1989_4_22_3_345_0}
}

Sekiguchi, T.; Oort, F.; Suwa, N. On the deformation of Artin-Schreier to Kummer. Annales scientifiques de l'École Normale Supérieure, Tome 22 (1989) pp. 345-375. doi : 10.24033/asens.1586. http://gdmltest.u-ga.fr/item/ASENS_1989_4_22_3_345_0/

[1] N. Bourbaki, Algèbre commutative, Eléments de Math., 27, 28, 30, 31, Hermann, Paris, 1961-1965.

[2] L. Breen, Extensions of Abelian Sheaves and Eilenberg-Maclane algebras, Invent. Math., Vol. 9, 1969, pp. 15-44. | MR 41 #3488 | Zbl 0181.26401

[3] L. Breen, Un théorème d'annulation pour certains des Exti de faisceaux abéliens, Ann. scient. Éc. Norm. Sup., Vol. 8, 1975, pp. 339-352. | Numdam | MR 53 #5595 | Zbl 0313.14001

[4] M. Demazure and P. Gabriel, Groupes algébriques, Tome 1. Masson, Paris, North-Holland Pub. Comp., Amsterdam, 1970. | Zbl 0203.23401

FGA A. Grothendieck, Fondements de la géométrie algébrique. Séminaire Bourbaki, 1952-1962, Secrétariat Math., Paris, 1962. | Zbl 0239.14002

GB A. Grothendieck, Le groupe de Brauer I, II, III. Dix exposés sur la cohomologie des schémas, North-Holland, Masson, 1968.

EGA A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique, Pub. Math. I.H.E.S., 1960-1967. | Numdam

SGA A. Grothendieck et al., Séminaire de géométrie algébrique, Lecture Notes in Math., Nos. 224, 269, 270, 305, Berlin-Heidelberg-New York, Springer-Verlag, 1971-1973.

[5] H. Hasse, Theorie der relativ-zyklischen algebraischen Funktionenkörper, insbesondere bei endlichen Konstantenkörper. Jour. reine angew. Math. (Crelle), 172, 1935, pp. 37-54. | JFM 60.0097.01 | Zbl 0010.00501

[6] J.-I. Igusa, Arithmetic Variety of Moduli for Genus Two, Ann. Math., 72, 1960, pp. 612-649. | MR 22 #5637 | Zbl 0122.39002

[7] T. Kambayashi and M. Miyanishi, On Flat Fibrations by the Affine Line, Illinois J. Math., No. 4, 22, 1978, pp. 662-671. | MR 80f:14028 | Zbl 0406.14012

[8] O. A. Laudal and K. Lønsted, Deformations of Curves I. Moduli for Hyperelliptic Curves. Algebraic Geometry, Proceedings Tromsø, Norway 1977, Lecture Notes in Math., No. 687, Berlin-Heidelberg-New York, Springer-Verlag, 1978, pp. 150-167. | Zbl 0422.14014

[9] D. Mumford, Geometric Invariant Theory. Ergebnisse, Berlin-Heidelberg-New York, Springer-Verlag, 1965. | MR 35 #5451 | Zbl 0147.39304

[10] D. Mumford, Abelian Varieties, Tata Inst. Studies in Math., Oxford University Press, 1970. | MR 44 #219 | Zbl 0223.14022

[11] M. Nagata, Local rings, Interscience Tracts in Pure & Applied Math., 131, J. Wiley, New York, 1962. | MR 27 #5790 | Zbl 0123.03402

[12] S. Nakajima, Action of an Automorphism of Order p on Cohomology Groups of an Algebraic Curves, J. Pure and Applied Alg. 42, 1986, pp. 85-94. | MR 88d:14018 | Zbl 0607.14022

[13] F. Oort, Commutative Group Schemes, Lecture Notes in Math., No. 15, Berlin-Heidelberg-New York, Springer-Verlag, 1966. | MR 35 #4229 | Zbl 0216.05603

[14] F. Oort, Finite Group Schemes, Local Moduli for Abelian Varieties and Lifting Problems, Compos. Math., Vol. 23, 1971, pp. 265-296 (Also : Algebraic Geometry, Oslo, 1970, F. Oort ed., Wolters-Noordhoff, 1972, pp. 223-254). | Numdam | MR 46 #186 | Zbl 0239.14018

[15] F. Oort, Singularities of coarse moduli schemes, Sém. Dubreil, 29, 1975/1976 ; Lecture Notes in Math., Vol. 586, pp. 61-76, Berlin-Heidelberg-New York, Springer-Verlag, 1977. | Zbl 0349.14003

[16] F. Oort and D. Mumford, Deformations and Liftings of Finite Commutative Group Schemes, Invent. Math., Vol. 5, 1968, pp. 317-334. | MR 37 #4085 | Zbl 0179.49901

[17] F. Oort and T. Sekiguchi, The canonical lifting of an ordinary Jacobian variety need not a Jacobian variety, J. Math. Soc. Japan, Vol. 38, 1986, pp. 427-437. | MR 87g:14047 | Zbl 0605.14031

[18] M. Raynaud, Spécialization du foncteur de Picard, I.H.E.S., Vol. 38, 1970, pp. 27-76. | Numdam | MR 44 #227 | Zbl 0207.51602

[19] P. Roquette, Abschötzung der Automorphismenzahl von Funktionenkörpern bei Primzahlcharakteristik, Math. Z., Vol. 117, 1970, pp. 157-163. | MR 43 #4826 | Zbl 0194.35302

[20] T. Sekiguchi and F. Oort, On the deformations of Witt groups to tori. In Algebraic and Topological Theories (to the memory of Dr. T. Miyarta), Kinokuniya Co., Ltd., 1985, pp. 283-298. | Zbl 0800.14023

[21] J.-P. Serre, Groupes algébriques et corps de classes, Hermann, Paris, 1959. | MR 21 #1973 | Zbl 0097.35604

[22] B. Singh, On the group of automorphisms of a function field of genus at least two, Jour. of Pure and Applied algebra, Vol. 4, 1974, pp. 205-229. | MR 50 #13047 | Zbl 0284.12007

[23] H. Stichtenoth, Uber die Automorphismengruppe eines algebraischen Funktionenkörpers von Primzahlcharakteristik. Teil I : Eine Abschötzung der Ordnung der Automorphismengruppe. Teil II : Ein spezieller typ von Funktionenkörpern, Arch. Math. Vol. 24, 1973, pp. 527-544 ; Vol. 25, 1973, pp. 615-631. | MR 53 #8068 | Zbl 0282.14007

[24] B. Weisfeiler, On a case of extensions of group schemes, Trans. Math. Soc., No. 1, 248, 1979, pp. 171-189. | MR 81c:14027 | Zbl 0412.14022

[25] W. Waterhouse and B. Weisfeiler, One-dimensional affine group schemes, J. of Alg., Vol. 66, 1980, pp. 550-568. | MR 82e:14057 | Zbl 0452.14013

[26] W. Waterhouse, A unified Kummer-Artin-Schreier sequence, Math. Ann., Vol. 277, 1987, pp. 447-451. | MR 88j:14058 | Zbl 0608.12026