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2 - Vector bundles on curves and p-adic Hodge theory

Published online by Cambridge University Press:  05 October 2014

Laurent Fargues
Institut de Mathématiques de Jussieu, Paris
Jean-Marc Fontaine
Université Paris Sud
Fred Diamond
King's College London
Payman L. Kassaei
King's College London
Minhyong Kim
University of Oxford
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Publisher: Cambridge University Press
Print publication year: 2014

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[1] Y., André. Slope filtrations. Confluentes Mathematici, 1:1–85, 2009.Google Scholar
[2] L., Berger. Représentations p-adiques et équations différentielles. Invent. Math., 148(2):219–284, 2002.Google Scholar
[3] Laurent, Berger. Construction de (φ, Γ)-modules: représentations p-adiques et B-paires. Algebra Number Theory, 2(1):91–120, 2008.Google Scholar
[4] F., Cherbonnier and P., Colmez. Représentations p-adiques surconvergentes. Invent. Math., 133(3):581–611, 1998.Google Scholar
[5] J.-F., Dat, S., Orlik, and M., Rapoport. Period domains over finite and p-adic fields, volume 183 of Cambridge Tracts in Mathematics. Cambridge University Press, 2010.
[6] Vladimir G., Drinfeld. Coverings of p-adic symmetric domains. Functional Analysis and its Applications, 10(2):29–40, 1976.Google Scholar
[7] G., Faltings. Group schemes with strict O-action. Mosc. Math. J., 2(2):249–279, 2002.Google Scholar
[8] G., Faltings. Coverings of p-adic period domains. J. Reine Angew. Math., 643:111–139, 2010.Google Scholar
[9] L., Fargues. L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld et applications cohomologiques. In L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld, Progress in math., 262, pages 1–325. Birkhäuser, 2008.
[10] L., Fargues. La filtration de Harder-Narasimhan des schémas en groupes finis et plats. J. Reine Angew. Math., 645:1–39, 2010.Google Scholar
[11] L., Fargues. La filtration canonique des points de torsion des groupes p-divisibles. Annales scientifiques de l'ENS, 44(6):905–961, 2011.Google Scholar
[12] L., Fargues and J.-M., Fontaine. Courbes et fibrés vectoriels en théorie de Hodge p-adique. Prépublication.
[13] L., Fargues and J.-M., Fontaine. Factorization of analytic functions in mixed characteristic. To appear in the proceedings of a conference in Sanya.
[14] L., Fargues and J.-M., Fontaine. Vector bundles and p-adic Galois representations. Stud. Adv. Math. 51, 2011.
[15] J.-M., Fontaine. Groupes p-divisibles sur les corps locaux. Société Mathématique de France, Paris, 1977. Astérisque, No. 47-48.
[16] J.-M., Fontaine. Le corps des périodes p-adiques. Astérisque, (223):59–111, 1994. With an appendix by Pierre Colmez, Périodes p-adiques (Bures-sur-Yvette, 1988).Google Scholar
[17] B., Gross and M., Hopkins. Equivariant vector bundles on the Lubin-Tate moduli space. In Topology and representation theory (Evanston, IL, 1992), volume 158 of Contemp. Math., pages 23–88. Amer. Math. Soc., 1994.
[18] A., Grothendieck. Sur la classification des fibrés holomorphes sur la sphère de Riemann. Amer. J. Math., 79:121–138, 1957.Google Scholar
[19] A., Grothendieck. Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents. I. Inst. Hautes Études Sci. Publ. Math., (11):167, 1961.Google Scholar
[20] U., Hartl and R., Pink. Vector bundles with a Frobenius structure on the punctured unit disc. Compos. Math., 140(3):689–716, 2004.Google Scholar
[21] K., Kedlaya. Slope filtrations revisited. Doc. Math., 10:447–525, 2005.Google Scholar
[22] K., Kedlaya. Slope filtrations for relative Frobenius. Astérisque, (319):259–301, 2008. Représentations p-adiques de groupes p-adiques. I. Représentations galoisiennes et (φ, Γ)-modules.Google Scholar
[23] K., Kedlaya, J., Pottharst, and L., Xiao. Cohomology of arithmetic families of (phi,gamma)-modules. arXiv:1203.5718v1.
[24] G., Laffaille. Groupes p-divisibles et corps gauches. Compositio Math., 56(2):221–232, 1985.Google Scholar
[25] M., Lazard. Les zéros des fonctions analytiques d'une variable sur un corps valué complet. Inst. Hautes Études Sci. Publ. Math., (14):47–75, 1962.Google Scholar
[26] B., Poonen. Maximally complete fields. Enseign. Math. (2), 39(1-2):87–106, 1993.Google Scholar
[27] M., Rapoport and T., Zink. Period spaces for p-divisible groups. Number 141 in Annals of Mathematics Studies. Princeton University Press, 1996.
[28] P., Schneider and J., Teitelbaum. Algebras of p-adic distributions and admissible representations. Invent. Math., 153(1):145–196, 2003.Google Scholar
[29] P., Scholze. Perfectoid spaces. Preprint.
[30] S., Sen. Continuous cohomology and p-adic Galois representations. Invent. Math., 62(1):89–116, 1980/81.Google Scholar
[31] J. T., Tate. p-divisible groups. In Proc. Conf. Local Fields (Driebergen, 1966), pages 158–183. Springer, 1967.
[32] J.-P., Wintenberger. Le corps des normes de certaines extensions infinies de corps locaux; applications. Ann. Sci. École Norm. Sup. (4), 16(1):59–89, 1983.Google Scholar
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