The image of the coefficient space in the universal deformation space of a flat Galois representation of a p-adic field
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Abstract
The coefficient space is a kind of resolution of singularities of the universal flat deformation space for a given Galois representation of some local field. It parametrizes (in some sense) the finite flat models for the Galois representation. The aim of this note is to determine the image of the coefficient space in the universal deformation space.
Mathematics Subject Classification (2000)
Primary: 11F80 Secondary: 11S20Preview
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References
- 1.Breuil C.: Integral p-adic Hodge Theory, Algebraic Geometry 2000. Azumino. Adv. Stud. Pure Math. 36, 51–80 (2002)MathSciNetGoogle Scholar
- 2.Conrad, B.: The flat deformation functor. In: Modular Forms and Fermat’s last Theorem (Boston, MA, 1995), pp. 373–420. Springer, New York (1997)Google Scholar
- 3.Fontaine, J-M.: Représentations p-adique des corps locaux. I., The Grothendieck Festschrift vol. II, Prog. Math. vol. 87, pp. 249–309. Birkhäuser Boston, Boston (1990)Google Scholar
- 4.Grothendieck, A., Dieudonné, J.: Élémentes de géométrie algèbrique, III, Inst. des Hautes Études. Sci. Publ. Math. 11 (1961), 17 (1963)Google Scholar
- 5.Hellmann E.: Connectedness of Kisin varieties for GL2. Adv. Math. 228, 219–240 (2011)MathSciNetMATHCrossRefGoogle Scholar
- 6.Kisin M.: Moduli of finite flat group schemes, and modularity. Ann. Math. 107(3), 1085–1180 (2009)MathSciNetCrossRefGoogle Scholar
- 7.Kisin M.: Modularity of 2-adic Barsotti-Tate representations. Invent. Math. 178(3), 587–634 (2009)MathSciNetMATHCrossRefGoogle Scholar
- 8.Kim, W.: Galois Deformation Theory for Norm Fields and their Arithmetic Applications, Ph.D. thesis, University of MichiganGoogle Scholar
- 9.Kim, W.: The classification of p-divisible groups over 2-adic discrete valuation rings. Preprint 2010, arXiv:1007.1904Google Scholar
- 10.Lau, E.: A relation between Dieudonne displays and crystalline Dieudonne theory, preprint 2010, arXiv:1006.2720.Google Scholar
- 11.Liu, T.: The Correspondence Between Barsotti-Tate Groups and Kisin Modules when p = 2. http://www.math.purdue.edu/~tongliu/research.html (2010).
- 12.Mazur, B.: An introduction to the deformation theory of Galois representations. In: Modular Forms and Fermat’s last Theorem (Boston, MA, 1995), pp. 243–311. Springer, New York (1997)Google Scholar
- 13.Pappas G., Rapoport M.: Local models in the ramified case I. The EL-case. J. Algebra Geom. 12, 107–145 (2003)MathSciNetMATHCrossRefGoogle Scholar
- 14.Pappas G., Rapoport M.: \({\Phi}\) -modules and coefficient spaces. Moscow Math. J. 9(3), 625–663 (2009)MathSciNetMATHGoogle Scholar
- 15.Ramakrishna R.: On a variation of Mazur’s deformation functor. Compos. Math. 87(3), 269–286 (1993)MathSciNetMATHGoogle Scholar
- 16.Raynaud M.: Schémas en groupes de type (p, . . . , p). Bull. Soc. Math. Fr. 102, 241–280 (1974)MathSciNetMATHGoogle Scholar
- 17.Serre J.-P.: Local Fields, Graduate Texts in Mathematics, vol 67. Springer, New York (1979)Google Scholar
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