Rank two filtered (𝜑,𝑁)-modules with Galois descent data and coefficients

Dousmanis, Gerasimos

doi:10.1090/S0002-9947-10-05100-7

Rank two filtered $(\varphi ,N)$-modules with Galois descent data and coefficients
HTML articles powered by AMS MathViewer

by Gerasimos Dousmanis PDF

Trans. Amer. Math. Soc. 362 (2010), 3883-3910 Request permission

Abstract:

Let $K$ be any finite extension of $\mathbb {Q}_{p},$ $L$ any finite Galois extension of $K$, and $E$ any finite large enough coefficient field containing $L.$ We classify two-dimensional $L$-semistable $E$-representations of $G_{K}$ by listing the isomorphism classes of rank two weakly admissible filtered $(\varphi ,N,L/K,E)$-modules.

References

Laurent Berger, An introduction to the theory of $p$-adic representations, Geometric aspects of Dwork theory. Vol. I, II, Walter de Gruyter, Berlin, 2004, pp. 255–292 (English, with English and French summaries). MR 2023292
Laurent Berger, Représentations $p$-adiques et équations différentielles, Invent. Math. 148 (2002), no. 2, 219–284 (French, with English summary). MR 1906150, DOI 10.1007/s002220100202
Christophe Breuil, Sur quelques représentations modulaires et $p$-adiques de $\textrm {GL}_2(\mathbf Q_p)$. II, J. Inst. Math. Jussieu 2 (2003), no. 1, 23–58 (French, with French summary). MR 1955206, DOI 10.1017/S1474748003000021
Christophe Breuil and Ariane Mézard, Multiplicités modulaires et représentations de $\textrm {GL}_2(\textbf {Z}_p)$ et de $\textrm {Gal}(\overline \textbf {Q}_p/\textbf {Q}_p)$ en $l=p$, Duke Math. J. 115 (2002), no. 2, 205–310 (French, with English and French summaries). With an appendix by Guy Henniart. MR 1944572, DOI 10.1215/S0012-7094-02-11522-1
Christophe Breuil and Peter Schneider, First steps towards $p$-adic Langlands functoriality, J. Reine Angew. Math. 610 (2007), 149–180. MR 2359853, DOI 10.1515/CRELLE.2007.070
Pierre Colmez and Jean-Marc Fontaine, Construction des représentations $p$-adiques semi-stables, Invent. Math. 140 (2000), no. 1, 1–43 (French). MR 1779803, DOI 10.1007/s002220000042
Brian Conrad, Fred Diamond, and Richard Taylor, Modularity of certain potentially Barsotti-Tate Galois representations, J. Amer. Math. Soc. 12 (1999), no. 2, 521–567. MR 1639612, DOI 10.1090/S0894-0347-99-00287-8
Dousmanis, Gerasimos On reductions of families of two-dimensional crystalline Galois representations. http://arxiv.org/abs/0805.1634 arXiv:0805.1634v3
Dousmanis, Gerasimos On reductions of families of two-dimensional crystalline Galois representations part II. http://arxiv.org/abs/0905.0080 arXiv:0905.0080v1
Jean-Marc Fontaine, Le corps des périodes $p$-adiques, Astérisque 223 (1994), 59–111 (French). With an appendix by Pierre Colmez; Périodes $p$-adiques (Bures-sur-Yvette, 1988). MR 1293971
Jean-Marc Fontaine, Représentations $l$-adiques potentiellement semi-stables, Astérisque 223 (1994), 321–347 (French). Périodes $p$-adiques (Bures-sur-Yvette, 1988). MR 1293977
Jean-Marc Fontaine and Barry Mazur, Geometric Galois representations, Elliptic curves, modular forms, & Fermat’s last theorem (Hong Kong, 1993) Ser. Number Theory, I, Int. Press, Cambridge, MA, 1995, pp. 41–78. MR 1363495
Fontaine, Jean-Marc; Ouyang, Yi Theory of $p$-adic Galois Representations. Forthcoming Springer book.
Eknath Ghate and Ariane Mézard, Filtered modules with coefficients, Trans. Amer. Math. Soc. 361 (2009), no. 5, 2243–2261. MR 2471916, DOI 10.1090/S0002-9947-08-04829-0
David Savitt, On a conjecture of Conrad, Diamond, and Taylor, Duke Math. J. 128 (2005), no. 1, 141–197. MR 2137952, DOI 10.1215/S0012-7094-04-12816-7
Maja Volkov, Les représentations $l$-adiques associées aux courbes elliptiques sur ${\Bbb Q}_p$, J. Reine Angew. Math. 535 (2001), 65–101 (French, with English summary). MR 1837096, DOI 10.1515/crll.2001.046