Crystalline boundedness principle
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 39 (2006) no. 2, pp. 245-300.
@article{ASENS_2006_4_39_2_245_0,
     author = {Vasiu, Adrian},
     title = {Crystalline boundedness principle},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {245--300},
     publisher = {Elsevier},
     volume = {Ser. 4, 39},
     number = {2},
     year = {2006},
     doi = {10.1016/j.ansens.2005.12.003},
     zbl = {05078685},
     mrnumber = {2245533},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.ansens.2005.12.003/}
}
TY  - JOUR
AU  - Vasiu, Adrian
TI  - Crystalline boundedness principle
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2006
DA  - 2006///
SP  - 245
EP  - 300
VL  - Ser. 4, 39
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.ansens.2005.12.003/
UR  - https://zbmath.org/?q=an%3A05078685
UR  - https://www.ams.org/mathscinet-getitem?mr=2245533
UR  - https://doi.org/10.1016/j.ansens.2005.12.003
DO  - 10.1016/j.ansens.2005.12.003
LA  - en
ID  - ASENS_2006_4_39_2_245_0
ER  - 
%0 Journal Article
%A Vasiu, Adrian
%T Crystalline boundedness principle
%J Annales scientifiques de l'École Normale Supérieure
%D 2006
%P 245-300
%V Ser. 4, 39
%N 2
%I Elsevier
%U https://doi.org/10.1016/j.ansens.2005.12.003
%R 10.1016/j.ansens.2005.12.003
%G en
%F ASENS_2006_4_39_2_245_0
Vasiu, Adrian. Crystalline boundedness principle. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 39 (2006) no. 2, pp. 245-300. doi : 10.1016/j.ansens.2005.12.003. http://www.numdam.org/articles/10.1016/j.ansens.2005.12.003/

[1] Borel A., Linear Algebraic Groups, Graduate Texts in Math., vol. 126, Springer, Berlin, 1991. | MR | Zbl

[2] Bosch S., Lütkebohmert W., Raynaud M., Néron Models, Ergeb. Math. Grenzgeb. (3), vol. 21, Springer, Berlin, 1990. | MR | Zbl

[3] Conway J.H., Curtis R.T., Norton S.P., Parker R.A., Wilson R.A., Atlas of Finite Groups, Oxford University Press, Eynsham, 1985, xxxiv+252 pp. | MR | Zbl

[4] Cremona J.E., Algorithms for Modular Elliptic Curves, Cambridge University Press, Cambridge, 1992. | MR | Zbl

[5] Demazure M., Lectures on p-Divisible Groups, Lecture Notes in Math., vol. 302, Springer, Berlin, 1972. | MR | Zbl

[6] Demazure M., Grothendieck A. et al. , Schémas en groupes, vols. I-III, Lecture Notes in Math., vols. 151-153, Springer, Berlin, 1970. | MR | Zbl

[7] Dieudonné J., Groupes de Lie et hyperalgèbres de Lie sur un corps de caractérisque p>0 (IV), Amer. J. Math. 77 (1955) 429-452. | Zbl

[8] De Jong J., Finite locally free group schemes in characteristic p and Dieudonné modules, Invent. Math. 114 (1) (1993) 89-137. | MR | Zbl

[9] De Jong J., Crystalline Dieudonné module theory via formal and rigid geometry, Inst. Hautes Études Sci. Publ. Math. 82 (1995) 5-96. | Numdam | MR | Zbl

[10] De Jong J., Oort F., Purity of the stratification by Newton polygons, J. Amer. Math. Soc. 13 (1) (2000) 209-241. | MR | Zbl

[11] Faltings G., Crystalline cohomology and p-adic Galois representations, in: Algebraic Analysis, Geometry, and Number Theory, Baltimore, MD, 1988, Johns Hopkins University Press, Baltimore, MD, 1989, pp. 25-80. | MR | Zbl

[12] Faltings G., Integral crystalline cohomology over very ramified valuation rings, J. Amer. Math. Soc. 12 (1) (1999) 117-144. | MR | Zbl

[13] Faltings G., Chai C.-L., Degeneration of Abelian Varieties, Ergeb. Math. Grenzgeb. (3), vol. 22, Springer, Berlin, 1990. | MR | Zbl

[14] Fontaine J.-M., Groupes p-divisibles sur les corps locaux, J. Astérisque, vol. 47/48, Soc. Math. de France, Paris, 1977. | MR | Zbl

[15] Fontaine J.-M., Laffaille G., Construction de représentations p-adiques, Ann. Sci. École Norm. Sup. 15 (4) (1982) 547-608. | Numdam | MR | Zbl

[16] Grothendieck A., Éléments de géométrie algébrique. II. Étude globale élémentaire de quelques classes de morphisms, Inst. Hautes Études Sci. Publ. Math., vol. 11, 1961. | Numdam | MR | Zbl

[17] Grothendieck A., Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents, Première partie, Inst. Hautes Études Sci. Publ. Math., vol. 11, 1963. | Numdam | MR

[18] Grothendieck A., Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schéma, Inst. Hautes Études Sci. Publ. Math., vol. 20, 1964, vol. 24, 1965, vol. 28, 1996, and vol. 32, 1967. | Numdam

[19] Grothendieck A., Groupes de Barsotti-Tate et cristaux de Dieudonné, Sém. Math. Sup., vol. 45, (1970), Les presses de l'Université de Montréal, Montréal, Quebec, 1974. | MR | Zbl

[20] Helgason S., Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978. | MR | Zbl

[21] Illusie L., Déformations des groupes de Barsotti-Tate (d'après A. Grothendieck), in: Seminar on Arithmetic Bundles: The Mordell Conjecture, Paris, 1983/84, J. Astérisque, vol. 127, Soc. Math. de France, Paris, 1985, pp. 151-198. | MR

[22] Katz N., Slope filtration of F-crystals, in: Journées de Géométrie Algébrique de Rennes, Rennes, 1978, vol. I, J. Astérisque, vol. 63, Soc. Math. de France, Paris, 1979, pp. 113-163. | MR | Zbl

[23] Katz N., Serre-Tate local moduli, in: Algebraic Surfaces Orsay, 1976-1978, Lecture Notes in Math., vol. 868, Springer, Berlin, 1981, pp. 138-202. | MR | Zbl

[24] Kottwitz R.E., Isocrystals with additional structure, Comp. Math. 56 (2) (1985) 201-220. | Numdam | MR | Zbl

[25] Kottwitz R.E., Points on some Shimura varieties over finite fields, J. Amer. Math. Soc. 5 (2) (1992) 373-444. | MR | Zbl

[26] Kraft, H., Kommutative algebraische p-Gruppen (mit Anwendungen auf p-divisible Gruppen und abelsche Varietäten), Manuscript, Univ. Bonn, 1975, 86 p.

[27] Li K.-Z., Oort F., Moduli of Supersingular Abelian Varieties, Lecture Notes in Math., vol. 1680, Springer, Berlin, 1998. | MR | Zbl

[28] Manin J.I., The theory of formal commutative groups in finite characteristic, Russian Math. Surveys 18 (6) (1963) 1-83. | MR | Zbl

[29] Matsumura H., Commutative Algebra, Benjamin/Cummings, Reading, MA, 1980. | MR | Zbl

[30] Messing W., The Crystals Associated to Barsotti-Tate Groups, with Applications to Abelian Schemes, Lecture Notes in Math., vol. 264, Springer, Berlin, 1972. | MR | Zbl

[31] Milne J.S., The points on a Shimura variety modulo a prime of good reduction, in: The Zeta Functions of Picard Modular Surfaces, Univ. Montréal Press, Montréal, Quebec, 1992, pp. 153-255. | MR | Zbl

[32] Mumford D., Abelian Varieties, Tata Inst. of Fund. Research Studies in Math., vol. 5, Tata Institute of Fundamental Research, Oxford University Press, Bombay, London, 1970, viii+242 pp. (Reprinted 1988). | MR | Zbl

[33] Mumford D., Fogarty J., Kirwan F., Geometric Invariant Theory, Ergeb. Math. Grenzgeb. (2), vol. 34, Springer, Berlin, 1994. | MR | Zbl

[34] Oort F., A stratification of a moduli space of abelian varieties, in: Moduli of Abelian Varieties, Texel Island, 1999, Progr. Math., vol. 195, Birkhäuser, Basel, 2001, pp. 345-416. | MR | Zbl

[35] Oort F., Newton polygon strata in the moduli space of abelian varieties, in: Moduli of Abelian Varieties, Texel Island, 1999, Progr. Math., vol. 195, Birkhäuser, Basel, 2001, pp. 417-440. | MR | Zbl

[36] Oort F., Foliations in moduli spaces of abelian varieties, J. Amer. Math. Soc. 17 (2) (2004) 267-296. | MR | Zbl

[37] Rapoport M., Richartz M., On the classification and specialization of F-isocrystals with additional structure, Comp. Math. 103 (2) (1996) 153-181. | Numdam | MR | Zbl

[38] Serre J.-P., Galois Cohomology, Springer, Berlin, 1997. | MR | Zbl

[39] Tate J., Classes d'isogénie des variétés sur un corps fini (d'après J. Honda), in: Sém. Bourbaki 1968/69, Exp. 352, Lecture Notes in Math., vol. 179, Springer, Berlin, 1971, pp. 95-110. | Numdam | Zbl

[40] Vasiu A., Integral canonical models of Shimura varieties of preabelian type, Asian J. Math. 3 (2) (1999) 401-518. | MR | Zbl

[41] Zink T., On the slope filtration, Duke Math. J. 109 (1) (2001) 79-95. | MR | Zbl

[42] Wintenberger J.-P., Un scindage de la filtration de Hodge pour certaines varietés algebriques sur les corps locaux, Ann. of Math. (2) 119 (3) (1984) 511-548. | MR | Zbl

Cited by Sources: