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1 - A semi-stable case of the Shafarevich Conjecture

Published online by Cambridge University Press:  05 October 2014

Victor Abrashkin
Affiliation:
University of Durham
Fred Diamond
Affiliation:
King's College London
Payman L. Kassaei
Affiliation:
King's College London
Minhyong Kim
Affiliation:
University of Oxford
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Publisher: Cambridge University Press
Print publication year: 2014

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References

[1] V. A., Abrashkin, Good reduction of two-dimensional Abelian varieties (Russian)Izv. Akad. Nauk SSSR Ser. Mat., 40 (1976), no. 2, 262–272Google Scholar
[2] V. A., Abrashkin, p-divisible groups over ℤ (Russian)Izv. Akad. Nauk SSSR Ser. Mat., 41 (1977), no. 5, 987–1007Google Scholar
[3] V. A., Abrashkin, Group schemes of period p over the ring of Witt vectors (Russian)Dokl. Akad. Nauk SSSR, 283 (1985), no. 6, 1289–1294Google Scholar
[4] V. A., Abrashkin, Honda systems of group schemes of period p (Russian)Izv. Akad. Nauk SSSR Ser. Mat., 51 (1987), no. 3, 451–484, 688; translation in Math. USSR-Izv. 30 (1988), no. 3, 419–453Google Scholar
[5] V. A., Abrashkin, Galois modules of group schemes of period p over the ring of Witt vectors (Russian)Izv. Akad. Nauk SSSR Ser. Mat., 51 (1987), no. 4, 691–736; translation in Math. USSR-Izv. 31 (1988), no. 1, 1–46Google Scholar
[6] V. A., Abrashkin, Modification of the Fontaine-Laffaille functor (Russian), Izv. Akad. Nauk SSSR Ser Mat, 53 (1989), 451–497; translation in Math. USSR-Izv., 34 (1990), 57–97Google Scholar
[7] V. A., Abrashkin, Modular representations of the Galois group of a local field and a generalization of a conjecture of Shafarevich (Russian)Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), no. 6, 1135–1182; translation in Math. USSR-Izv. 35 (1990), no. 3, 469–518Google Scholar
[8] V. A., Abrashkin, A ramification filtration of the Galois group of a local field. III. (Russian)Izv. Ross. Akad. Nauk Ser. Mat. 62 (1998), no. 5, 3–48; translation in Izv. Math. 62 (1998), no. 5, 857–900Google Scholar
[9] V., Abrashkin, Galois modules arising from Faltings' strict modules. Compos. Math. 142 (2006), no. 4, 867–888Google Scholar
[10] V., Abrashkin, Characteristic p analogue of modules with finite crystalline height, Pure Appl. Math. Q., 5 (2009), 469–494Google Scholar
[11] V., Abrashkin, Projective varieties with bad reduction at 3 only, Doc. Math. 18 (2013), 547–619.Google Scholar
[12] Algebraic number theory. Proceedings of an instructional conference organized by the LMS. Edited by J. W. S., Cassels and A. Fröhlich Academic Press, London; Thompson Book Co., Inc., Washington, D.C. 1967
[13] A., Brumer, K., KramerNon-existence of certain semistable abelian varieties, Manuscripta Math., 106 (2001), 291–304Google Scholar
[14] Ch., Breuil, Construction de représentations p-adiques semi-stable, Ann. Sci. École Norm. Sup., 4 Ser., 31 (1998), 281–327Google Scholar
[15] Ch., Breuil, Représentations semi-stables et modules fortement divisibles, Invent. Math., 136 (1999), 89–122Google Scholar
[16] Ch., Breuil, Integral p-adic Hodge theory, Adv. Stud. Pure Math. 36 (2002), 51–80Google Scholar
[17] P., Deligne, Les corps locaux de caractristique p, limites de corps locaux de caractristique 0. (French) Representations of reductive groups over a local field, 119–157, Travaux en Cours, Hermann, Paris, 1984
[18] Dia Y, Diaz, Tables minorant la racine n-ième du discriminant d'un corps de degré n Publications Mathematiques d'Orsay, 80.06, Université de Paris-Sud, Départment de Mathématique, Bat. 425, 91405, Orsay, France
[19] J.-M., Fontaine, G., Laffaille, Construction de représentations p-adiques, Ann. Sci. École Norm. Sup., 4 Ser. 15 (1982), 547–608Google Scholar
[20] J.-M., Fontaine, Groupes finis commutatifs sur les vecteurs de Witt, C. R. Acad. Sci. Paris Sér. A-B 280 (1975), A1423A1425Google Scholar
[21] J.-M., Fontaine, Il n'y a pas de variété abélienne sur ℤ, Invent. Math., 81 (1985), 515–538Google Scholar
[22] J.-M., Fontaine, W., Messing, p-adic periods and p-adic étale cohomology. In: Current Trends in Arithmetical Algebraic Geometry, K., Ribet, Editor, Contemporary Math. 67, Amer. Math. Soc., Providence (1987), 179–207
[23] J.-M., Fontaine, Schémas propres et lisses sur ℤ. Proceedings of the Indo-French Conference on Geometry (Bombay, 1989), 43–56, Hindustan Book Agency, Delhi, 1993
[24] Sh., Hattori, On a ramification bound of torsion semi-stable representations over a local field, J. Number theory, 129 (2009), 2474–2503Google Scholar
[25] J., Martinet, Petits discriminants des corps de nombres, London Math. Soc -Lect. note ser., 56 (1982), 151–193
[26] W., MessingThe crystals associated to Barsotti-Tate groups: with applications to abelian schemes, Lecture notes in Mathematics. 264, Springer-Verlag, 1972
[27] R., Schoof, Abelian varieties over ℚ with bad reduction in one prime only. Comp. Math., 141 (2005), 847–868.Google Scholar
[28] J.-P., Serre, Local FieldsBerlin, New York: Springer-Verlag, 1980
[29] I. R., Shafarevich, Algebraic number fields. Proc. Internat. Congr. Math. (Stockholm, 1962), Inst. Mittag-Leffler, Djursholm, (1963), 163–176
[30] G., Poitou, Minorations de discriminants (d'apr A. M. Odlyzko). Séminaire Bourbaki, Vol. 1975/76 28me anne, Exp. No. 479, pp. 136–153. Lecture Notes in Math., 567, Springer, Berlin, 1977 Berlin, New York: Springer-Verlag, 1980
[31] J., Tate, p-divisible groups, Proc. Conf. Local Fields (Dreibergen, 1966), Springer-Verlag, Berlin and New-York, 1967, pp. 158–183
[32] J.-P., Wintenberger, Le corps des normes de certaines extensions infinies des corps locaux; applicationAnn. Sci. Ec. Norm. Super., IV. Ser, 16 (1983), 59–89Google Scholar
[33] J.-P., Wintenberger, Extensions de Lie et groupes d'automorphismes des corps locaux de caractristique p. (French)C. R. Acad. Sci. Paris Sér. A-B 288 (1979), no. 9, A477–A479Google Scholar

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