On Deformations of 1-motives
Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 11-22

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2017-076-2
Mots-clés : 1-motive, Barsotti-Tate group
Bertapelle, A.; Mazzari, N. On Deformations of 1-motives. Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 11-22. doi: 10.4153/CMB-2017-076-2
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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, 1919–1944. . Google Scholar | DOI

[2] Andreatta, F. and Barbieri-Viale, L., Crystalline realizations of 1-motives . Math. Ann. 331(2005), 111–172. . Google Scholar | DOI

[3] Bertapelle, A. and González-Avilés, C. D., The Greenberg functor revisited. Eur. J. Math. (2018). . Google Scholar | DOI

[4] Deligne, P., Théorie de Hodge. III . Inst. Hautes Études Sci. Publ. Math. 44(1974), 5–77.10.1007/BF02685881 Google Scholar

[5] Greenberg, M. J., Schemata over local rings. II . Ann. of Math. 78(1963), 256–266. . Google Scholar | DOI

[6] 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

[7] Madapusi Sampath, K. S., Toroidal compactifications of integral models of Shimura varieties of Hodge type. PhD thesis, Chicago, 2011. Google Scholar

[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, 1972.10.1007/BFb0058301 Google Scholar

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