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On Deformations of 1-motives

Part of: Cycles and subschemes Algebraic groups

Published online by Cambridge University Press:  04 January 2019

A. Bertapelle  and
N. Mazzari
A. Bertapelle
Affiliation:
Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, via Trieste, 63, I-35121 Padova, Italy Email: [email protected]
N. Mazzari
Affiliation:
Institut de Mathématiques de Bordeaux, University of Bordeaux, F-33405 Talence cedex, France Email: [email protected]
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Abstract

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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.

Keywords

1-motiveBarsotti-Tate group

MSC classification

Primary: 14L15: Group schemes
Secondary: 14C15: (Equivariant) Chow groups and rings; motives 14L05: Formal groups, $p$-divisible groups
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 1 , March 2019 , pp. 11 - 22
Copyright
© Canadian Mathematical Society 2018 

References

Andreatta, F. and Bertapelle, A., Universal extension crystals of 1-motives and applications . J. Pure Appl. Algebra 215(2011), no. 8, 1919–1944. https://doi.org/10.1016/j.jpaa.2010.11.004.Google Scholar
Andreatta, F. and Barbieri-Viale, L., Crystalline realizations of 1-motives . Math. Ann. 331(2005), 111–172. https://doi.org/10.1007/s00208-004-0576-4.Google Scholar
Bertapelle, A. and González-Avilés, C. D., The Greenberg functor revisited. Eur. J. Math. (2018). https://doi.org/10.1007/s40879-017-0210-0.Google Scholar
Deligne, P., Théorie de Hodge. III . Inst. Hautes Études Sci. Publ. Math. 44(1974), 5–77.10.1007/BF02685881Google Scholar
Greenberg, M. J., Schemata over local rings. II . Ann. of Math. 78(1963), 256–266. https://doi.org/10.2307/1970342.Google Scholar
Katz, N., Serre–Tate local moduli . In: Algebraic surfaces (Orsay, 1976–78), Lecture Notes in Math., 868, Springer, Berlin-New York, 1981, pp. 138–202.Google Scholar
Madapusi Sampath, K. S., Toroidal compactifications of integral models of Shimura varieties of Hodge type. PhD thesis, Chicago, 2011.Google Scholar
Messing, W., The crystals associated to Barsotti–Tate groups with applications to abelian schemes. Lecture Notes in Mathematics, 264, Springer-Verlag, Berlin-New York, 1972.10.1007/BFb0058301Google Scholar