Finite group schemes, local moduli for abelian varieties, and lifting problems

Frans Oort

Compositio Mathematica (1971)

  • Volume: 23, Issue: 3, page 265-296
  • ISSN: 0010-437X

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Oort, Frans. "Finite group schemes, local moduli for abelian varieties, and lifting problems." Compositio Mathematica 23.3 (1971): 265-296. <http://eudml.org/doc/89089>.

@article{Oort1971,
author = {Oort, Frans},
journal = {Compositio Mathematica},
language = {eng},
number = {3},
pages = {265-296},
publisher = {Wolters-Noordhoff Publishing},
title = {Finite group schemes, local moduli for abelian varieties, and lifting problems},
url = {http://eudml.org/doc/89089},
volume = {23},
year = {1971},
}

TY - JOUR
AU - Oort, Frans
TI - Finite group schemes, local moduli for abelian varieties, and lifting problems
JO - Compositio Mathematica
PY - 1971
PB - Wolters-Noordhoff Publishing
VL - 23
IS - 3
SP - 265
EP - 296
LA - eng
UR - http://eudml.org/doc/89089
ER -

References

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  2. M. Demazure et A. Grothendieck Sgad - Schémas en groupes. Sém. de géom. algébrique, 1963-1964, IHES. 
  3. P. Gabriel [2] - Des catégories abéliennes. Bull. Soc. Math. France, 90 (1962), 323-448. Zbl0201.35602MR232821
  4. A. Grothendieck et J. Dieudonné Ega - Eléments de géométrie algébrique. Publ. Math...., 1960,... 
  5. A. Grothendieck Sga - Sém. de géom. algébrique1960, IHES. 
  6. A. Grothendieck Fga - Fondements de la géométrie algébrique. Extraits du Sém. Bourbaki, 1957-1962. Secr. Math., Paris, 1962. Zbl0239.14002MR146040
  7. K. Kodaira and D.C. Spencer [3] - On deformations of complex analytic structures I and II. Ann. Math.67 (1958), 328-401 and 403-466. Zbl0128.16901MR112154
  8. S. Lang Lav - Abelian varieties. Intersc. Tracts, N.7, Intersc. Publ.1959. Zbl0098.13201MR106225
  9. A.H.M. Levelt [4] - Sur la proreprésentabilité de certain foncteurs en géométrie algébrique. Multigraphed notes, Kath. Univ. Nijmegen, The Netherlands, 1964? 
  10. D. Mumford Git - Geometric invariant theory. Ergebnisse der Math., Bd. 34, Springer Verlag, 1965. Zbl0147.39304MR214602
  11. D. Mumford [5] - Bi-extensions of formal groups. Alg. geom., papers presented at the Bombay Colloq.1968, Tata Inst.stud. in math. vol. 4, Oxford Univ. Press1969, pp. 307-322. Zbl0216.33101MR257089
  12. D. Mumford Mav - Abelian varieties. Tata Inst. stud. in math. vol. 5, Oxford Univ. Press, 1970. Zbl0223.14022MR282985
  13. J.P. Murre [6] - On contravariant functors from the category of preschemes over a field into the category of abelian groups. Publ. IHES No. 23 (1964). Zbl0142.18402
  14. M. Nagata [7] - Local rings. Intersc. Tracts, No. 13. Intersc. Publ.1962. Zbl0123.03402MR155856
  15. F. Oort Cgs - Commutative group schemes. Lect. N. Math. N.15, Springer Verlag, 1966. Zbl0216.05603MR213365
  16. F. Oort and D. Mumford [8] - Deformations and liftings of finite commutative group schemes. Inv. math.5 (1968), 317-334. Zbl0179.49901MR228505
  17. M. Raynaud [9] - Faisceaux amples sur les schémas en groups et les espaces homogènes. Lect. N. Math. N.119, Springer Verlag, 1970. Zbl0195.22701MR260758
  18. M. Schlessinger [10] - Functors of artin rings. Transact. Amer. Math. Soc.130 (1968), 208-222. Zbl0167.49503MR217093
  19. [11] - Sém. de géom. algébrique, Fac. Sc.Orsay1967-1968. 
  20. J.-P. Serre GA- Groupes algébriques et corps de classes. Act. Sc. Ind.1264, HermannParis, 1959. Zbl0097.35604
  21. J.-P. Serre [12] - Quelques propriétés des variétés abéliennes en caractéristique p. Amer. J. Math.80 (1958), 715-739. Zbl0099.16201MR98100
  22. J.-P. Serre [13] - Exemples de variétés projectives en caractéristiques p non relevable en caractéristique zéro. Proc. Nat. Acad. Sc. USA, 47 (1961), 108-109. Zbl0100.16701MR132067
  23. J. Tate and F. Oort [14] - Group schemes of prime order. Ann. Ec. Norm. Sup.2 (1969), 1-21. Zbl0195.50801MR265368

Citations in EuDML Documents

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  1. Pierre Deligne, Georgios Pappas, Singularités des espaces de modules de Hilbert, en les caractéristiques divisant le discriminant
  2. Tsutomu Sekiguchi, Wild ramification of moduli spaces for curves or for abelian varieties
  3. Jean Fresnel, Marius Van Der Put, Uniformisation de variétés de Jacobi et déformations de courbes
  4. Eyal Z. Goren, Kristin E. Lauter, Class Invariants for Quartic CM Fields
  5. T. Sekiguchi, F. Oort, N. Suwa, On the deformation of Artin-Schreier to Kummer

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