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.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Breuil C.: Integral p-adic Hodge Theory, Algebraic Geometry 2000. Azumino. Adv. Stud. Pure Math. 36, 51–80 (2002)
Conrad, B.: The flat deformation functor. In: Modular Forms and Fermat’s last Theorem (Boston, MA, 1995), pp. 373–420. Springer, New York (1997)
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)
Grothendieck, A., Dieudonné, J.: Élémentes de géométrie algèbrique, III, Inst. des Hautes Études. Sci. Publ. Math. 11 (1961), 17 (1963)
Hellmann E.: Connectedness of Kisin varieties for GL2. Adv. Math. 228, 219–240 (2011)
Kisin M.: Moduli of finite flat group schemes, and modularity. Ann. Math. 107(3), 1085–1180 (2009)
Kisin M.: Modularity of 2-adic Barsotti-Tate representations. Invent. Math. 178(3), 587–634 (2009)
Kim, W.: Galois Deformation Theory for Norm Fields and their Arithmetic Applications, Ph.D. thesis, University of Michigan
Kim, W.: The classification of p-divisible groups over 2-adic discrete valuation rings. Preprint 2010, arXiv:1007.1904
Lau, E.: A relation between Dieudonne displays and crystalline Dieudonne theory, preprint 2010, arXiv:1006.2720.
Liu, T.: The Correspondence Between Barsotti-Tate Groups and Kisin Modules when p = 2. http://www.math.purdue.edu/~tongliu/research.html (2010).
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)
Pappas G., Rapoport M.: Local models in the ramified case I. The EL-case. J. Algebra Geom. 12, 107–145 (2003)
Pappas G., Rapoport M.: \({\Phi}\) -modules and coefficient spaces. Moscow Math. J. 9(3), 625–663 (2009)
Ramakrishna R.: On a variation of Mazur’s deformation functor. Compos. Math. 87(3), 269–286 (1993)
Raynaud M.: Schémas en groupes de type (p, . . . , p). Bull. Soc. Math. Fr. 102, 241–280 (1974)
Serre J.-P.: Local Fields, Graduate Texts in Mathematics, vol 67. Springer, New York (1979)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hellmann, E. The image of the coefficient space in the universal deformation space of a flat Galois representation of a p-adic field. manuscripta math. 139, 273–290 (2012). https://doi.org/10.1007/s00229-011-0515-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-011-0515-0