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On Deformations of 1-motives

  • A. Bertapelle (a1) and N. Mazzari (a2)
Abstract

According to a well-known theorem of Serre and Tate, the infinitesimal deformation theory of an abelian variety in positive characteristic is equivalent to the infinitesimal deformation theory of its Barsotti–Tate group. We extend this result to 1-motives.

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References
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[1] Andreatta, F. and Bertapelle, A., Universal extension crystals of 1-motives and applications . J. Pure Appl. Algebra 215(2011), no. 8, 19191944. https://doi.org/10.1016/j.jpaa.2010.11.004.
[2] Andreatta, F. and Barbieri-Viale, L., Crystalline realizations of 1-motives . Math. Ann. 331(2005), 111172. https://doi.org/10.1007/s00208-004-0576-4.
[3] Bertapelle, A. and González-Avilés, C. D., The Greenberg functor revisited. Eur. J. Math. (2018). https://doi.org/10.1007/s40879-017-0210-0.
[4] Deligne, P., Théorie de Hodge. III . Inst. Hautes Études Sci. Publ. Math. 44(1974), 577.
[5] Greenberg, M. J., Schemata over local rings. II . Ann. of Math. 78(1963), 256266. https://doi.org/10.2307/1970342.
[6] Katz, N., Serre–Tate local moduli . In: Algebraic surfaces (Orsay, 1976–78), Lecture Notes in Math., 868, Springer, Berlin-New York, 1981, pp. 138202.
[7] Madapusi Sampath, K. S., Toroidal compactifications of integral models of Shimura varieties of Hodge type. PhD thesis, Chicago, 2011.
[8] Messing, W., The crystals associated to Barsotti–Tate groups with applications to abelian schemes. Lecture Notes in Mathematics, 264, Springer-Verlag, Berlin-New York, 1972.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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