Ramification and moduli spaces of finite flat models
Annales de l'Institut Fourier, Volume 61 (2011) no. 5, p. 1943-1975

We determine the type of the zeta functions and the range of the dimensions of the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This gives a generalization of Raynaud’s theorem on the uniqueness of finite flat models in low ramifications.

Nous déterminons le type des fonctions zéta et la gamme des dimensions des espaces des modules des modèles plats finis des représentations galoisiennes locales à deux dimensions sur corps finis. Cela donne une généralisation du théorème de Raynaud sur l’unicité de modèles plats finis dans les petites ramifications.

DOI : https://doi.org/10.5802/aif.2662
Classification:  11F80,  14D20
Keywords: Group scheme, moduli space, p-adic field
@article{AIF_2011__61_5_1943_0,
     author = {Imai, Naoki},
     title = {Ramification and moduli spaces of finite flat models},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {5},
     year = {2011},
     pages = {1943-1975},
     doi = {10.5802/aif.2662},
     mrnumber = {2961844},
     zbl = {1279.11112},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2011__61_5_1943_0}
}
Imai, Naoki. Ramification and moduli spaces of finite flat models. Annales de l'Institut Fourier, Volume 61 (2011) no. 5, pp. 1943-1975. doi : 10.5802/aif.2662. http://www.numdam.org/item/AIF_2011__61_5_1943_0/

[1] Imai, Naoki On the connected components of moduli spaces of finite flat models, Amer. J. of Math., Tome 132 (2010) no. 5, pp. 1189-1204 | Article | MR 2732343 | Zbl 1205.14025

[2] Kisin, Mark Moduli of finite flat group schemes, and modularity, Ann. of Math. (2), Tome 170 (2009) no. 3, pp. 1085-1180 | Article | MR 2600871 | Zbl 1201.14034

[3] Raynaud, Michel Schémas en groupes de type (p,,p), Bull. Soc. Math. France, Tome 102 (1974), pp. 241-280 | Numdam | MR 419467 | Zbl 0325.14020