Ir al contenido

Documat

Infinitesimal characters in arithmetic families

  • Gabriel Dospinescu [1] ; Vytautas Paškūnas [2] ; Benjamin Schraen [3]
    1. [1] University of Clermont Auvergne

      University of Clermont Auvergne

      Arrondissement de Clermont-Ferrand, Francia

    2. [2] University of Duisburg-Essen

      University of Duisburg-Essen

      Kreisfreie Stadt Essen, Alemania

    3. [3] Claude Bernard University Lyon 1

      Claude Bernard University Lyon 1

      Arrondissement de Lyon, Francia

    Mostrar afiliaciones +
  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 4, 2025
  • Idioma: inglés
  • DOI: 10.1007/s00029-025-01045-6
  • Enlaces
  • Resumen

    • We associate infinitesimal characters to (twisted) families of L-parameters and C-parameters of p-adic reductive groups. We use the construction to study the action of the centre of the universal enveloping algebra on the locally analytic vectors in the Hecke eigenspaces in the completed cohomology.

  • Referencias bibliográficas
    • Ardakov, K., Wadsley, S.: On irreducible representations of compact p-adic analytic groups. Annals of Mathematics 178, 453–557 (2013)
    • Bellovin, R.: p-adic Hodge theory in rigid analytic families. Algebra Number Theory 9(2), 371–433 (2015)
    • Berger, L., Colmez, P.: Familles de représentations de de Rham et monodromie p-adique, Représentations p-adiques de groupes p-adiques. I....
    • Borel, A.: Automorphic L-functions, Automorphic Forms, Representations and L-functions, (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis,...
    • Borel, A.: Linear Algebraic Groups, 2nd edn. Springer (1991)
    • Borel, A.: Automorphic forms on reductive groups. Automorphic forms and applications, 7–39, IAS/Park City Math. Ser., 12, Amer. Math. Soc.,...
    • Borel, A., Wallach, N.: Continuous cohomology, discrete subgroups, and representations of reductive groups, second ed., Mathematical Surveys...
    • Bosch, S., Güntzer, U., Remmert, R.: Non-Archimedean analysis, Grundlehren der Mathematischen Wissenschaften, 261. Springer-Verlag, Berlin,...
    • Bourbaki, N.: Commutative Algebra. Springer (1989)
    • Breen, L., Messing, W.: Differential geometry of gerbes. Adv. Math. 198(2), 732–846 (2005)
    • Breuil, C., Hellmann, E., Schraen, B.: Une interprétation modulaire de la variété trianguline. Math. Annalen 367, 1587–1645 (2017)
    • Buzzard, K., Gee, T.: The conjectural connections between automorphic representations and Galois representations. arXiv:1009.0785v3, (2015)
    • Calegari, F., Emerton, M.: Completed cohomology - a survey, pp. 239–257. CUP, Non-abelian fundamental groups and Iwasawa theory (2011)
    • Calegari, F., Geraghty, D.: Modularity lifting beyond the Taylor-Wiles method. Inventiones Mathematicae 211(1), 297–433 (2018)
    • Caraiani, A., Emerton, M., Gee, T., Geraghty, D., Paškūnas, V., Shin, S.W.: Patching and the p-adic Langlands program. Cambridge J. Math....
    • Caraiani, A., Scholze, P.: On the generic part of the cohomology of compact Shimura varieties. Annals of Mathematics 186, 649–766 (2017)
    • Carayol, H.: Sur les représentations p-adiques associées aux formes modulaires de Hilbert. Ann. Sci. École Norm. Sup. (4) 19(3), 409–468 (1986)
    • Chenevier, G.: Familles p-adiques de formes automorphes pour GL(n). Journal für die reine und angewandte Mathematik 570, 143–217 (2004)
    • Chenevier, G.: The p-adic analytic space of pseudocharacters of a profinite group, and pseudorepresentations over arbitrary rings, London...
    • Chenevier, G., Harris, M.: Construction of automorphic Galois representations. II. Camb. J. Math. 1(1), 53–73 (2013)
    • Clozel, L., Harris, M., Taylor, R.: Automorphy for some l-adic lifts of automorphic mod l Galois representations, Pub. Math. I.H.É.S. 108,...
    • Colmez, P.: Représentations de GL2(Qp) et (ϕ, )-modules. Astérisque 330, 281–509 (2010)
    • Colmez, P., Dospinescu, G., Paškūnas, V.: The p-adic local Langlands correspondence for GL2(Qp). Camb. J. Math. 2(1), 1–47 (2014)
    • Conrad, B.: Reductive group schemes. Autour des schémas en groupes. Vol. I, 93–444, Panor. Synthèses, 42/43, Soc. Math. France, Paris, (2014)
    • Deligne, P., Milne, J.S.: Tannakian Categories, in Hodge Cycles, Motives, and Shimura Varieties, LNM 900, Springer, 101–228 (1982)
    • Demailly, J.-P.: Complex Analytic and Differential Geometry, available at https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf
    • Dixmier, J.: Enveloping algebras. Revised reprint of the 1977 translation. Graduate Studies in Mathematics, 11. American Mathematical Society,...
    • Dospinescu, G.: Actions infinitésimales dans la correspondance de Langlands locale p-adique. Mathematische Annalen 354, 627–657 (2012)
    • Dospinescu, G., Paškūnas, V., Schraen, B.: Gelfand-Kirillov dimension and the p-adic Jacquet-Langlands correspondence. J. Reine Angew. Math....
    • Dospinescu, G., Schraen, B.: Endomorphism algebras of admissible p-adic representations of p-adic Lie groups. Representation Theory 17, 237–246...
    • Emerton, M.: Locally analytic vectors in representations of locally p-adic analytic groups, to appear in Memoirs of the AMS
    • Emerton, M.: On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms. Invent. Math. 164(1), 1–84 (2006)
    • Emerton, M.: Local-global compatibility in the p-adic Langlands programme for GL2/Q, preprint (2011)
    • Emerton, M.: Completed cohomology and the p-adic Langlands program. Proceedings of the International Congress of Mathematicians–Seoul 2014....
    • Emerton, M., Gee, T., Herzig, F.: Weight cycling and Serre-type conjectures for unitary groups. Duke Math. J. 162(9), 1649–1722 (2013)
    • Emerton, M., Paškūnas, V.: On the density of supercuspidal points of fixed regular weight in local deformation rings and global Hecke algebras....
    • Faltings, G.: Hodge-Tate structures and modular forms. Math. Ann. 278, 133–149 (1987)
    • Fintzen, J., Shin, S.W.: Congruences of algebraic automorphic forms and supercuspidal representations. Cambridge Journal of Mathematics 9(2),...
    • Franke, J.: Harmonic analysis in weighted L2–spaces. Ann. scient. Ec. Norm. Sup., 4e série 31, 181–279 (1998)
    • Franke, J., Schwermer, J.: A decomposition of spaces of automorphic forms, and the Eisenstein cohomology of arithmetic groups. Math. Ann....
    • Fresnel, J., van der Put, M.: Rigid Analytic Geometry and Its Applications, Progress in Mathematics 218, Birkhäuser, (2004)
    • Gee, T., Herzig, F., Liu, T., Savitt, D.: Potentially crystalline lifts of certain prescribed types. Documenta Mathematica 22, 397–422 (2017)
    • Gee, T., Newton, J.: Patching and the completed homology of locally symmetric spaces. Journal de l’Institut de Mathématiques de Jussieu 21(2),...
    • Hansen, D., Johansson, C.: Perfectoid Shimura varieties and the Calegari–Emerton conjectures. J. Lond. Math. Soc. (2) 108 (2023), no. 5, 1954–(2000)
    • Harish-Chandra: Lie algebras and the Tannaka duality theorem. Ann. of Math. (2) 51, 299–330 (1950)
    • Helmann, E., Schraen, B.: Density of potentially crystalline representations of fixed weight. Compos. Math. 152, 1609–1647 (2016)
    • Hill, R.: On Emerton’s p-adic Banach Spaces. International Mathematics Research Notices 18, 3588–3632 (2010)
    • Hotta, R., Takeuchi, K., Tanisaki, T.: D-Modules, Perverse Sheaves and Representation Theory, Progress in Mathematics 236, Birkhäuser Boston,...
    • Howe, S.: The p-adic Jacquet-Langlands correspondence and a question of Serre. Compos. Math. 158(2), 245–286 (2022)
    • Humphreys, J.E.: Introduction to Lie algebras and representation theory. Graduate Texts in Mathematics, Vol. 9. Springer-Verlag, New York-Berlin,...
    • Humphreys, J.E.: Reflection groups and Coxeter groups. Cambridge Studies in Advanced Mathematics, 29. Cambridge University Press, Cambridge,...
    • Jantzen, J.C.: Representations of algebraic groups, Mathematical Surveys and Monographs, Volume: 107; 576 pp (2003) de Jong, A.J.: Crystalline...
    • Knapp, A.W.: Representation theory of semisimple groups. An overview based on examples. Reprint of the 1986 original. Princeton Landmarks...
    • Knight, E.: A p-adic Jacquet–Langlands correspondence, http://www.math.toronto.edu/~eknight/ Thesis.pdf
    • Langlands, R.P.: On the classification of representations of real algebraic groups, in Representation Theory and harmonic analysis on semisimple...
    • Lazard, M.: Groupes analytiques p-adiques. Inst. Hautes Études Sci. Publ. Math. No. 26, 389–603 (1965)
    • Matsumura, H.: Commutative ring theory, Second edition, Cambridge Studies in Advanced Mathematics, 8. CUP, Cambridge (1989)
    • Milne, J.S.: Semisimple Lie Algebras, Algebraic Groups and Tensor Categories, Notes dated May 9, 2007 available at www.jmilne.org/math/articles/2007a.pdf
    • Newton, J.: Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence. Math. Ann. 355, 729–763 (2013)
    • Pan, L.: On locally analytic vectors of the completed cohomology of modular curves. Forum Math. Pi 10, Paper No. e7, 82 pp (2022)
    • Paškūnas, V.: The image of Colmez’s Montreal functor. Publ. Math. Inst. Hautes Études Sci. 118, 1–191 (2013)
    • Paškūnas, V.: On the Breuil-Mézard Conjecture. Duke Math. J. 164(2), 297–359 (2015)
    • Paškūnas, V.: Blocks for mod p representations of GL2(Qp), Automorphic forms and Galois representations, Vol. 2, 231–247, London Math. Soc....
    • Paškūnas, V.: On 2-dimensional 2-adic Galois representations of local and global fields. Algebra Number Theory 10(6), 1301–1358 (2016)
    • Paškūnas, V.: A note on Galois representations associated to automorphic forms, Appendix C to [38]
    • Paškūnas, V.: On some consequences of a theorem of J. Ludwig. J. Inst. Math. Jussieu 21(3), 1067–1106 (2022)
    • Patrikis, S.: Variations on a theorem of Tate. Memoirs of AMS, 258(1238) (2019)
    • Platonov, V., Rapinchuk, A.: Algebraic Groups and Number Theory, Academic Press Inc., (1994)
    • Sansuc, J.-J.: Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres. Journal für die reine und angewandte...
    • Schneider, P.: Nonarchimedean Functional Analysis. Springer (2002)
    • Schneider, P.: p-adic Lie groups, Grundlehren der mathematischen Wissenschaften 344, Springer (2011)
    • Schneider, P., Teitelbaum, J.: Algebras of p-adic distributions and admissible representations. Invent. math. 153, 145–196 (2003)
    • Schneider, P., Teitelbaum, J.: Locally analytic distributions and p-adic representation theory, with applications to GL2
    • Scholze, P.: On the p-adic cohomology of the Lubin-Tate tower. Ann. Sci. Éc. Norm. Supér. (4) 51(4), 811–863 (2018)
    • Sen, S.: Continuous Cohomology and p-Adic Galois Representations. Inventiones mathematicae (1980/81) Volume 62, 89–116
    • Serre, J.-P.: Groupes de Grothendieck des schémas en groupes réductifs déployés. Inst. Hautes Études Sci. Publ. Math. No. 34, 37–52 (1968)
    • Serre, J.-P.: Lie algebras and Lie groups. Springer (1992)
    • Serre, J.-P.: Groupes algébriques associés aux modules de Hodge-Tate. Astérisque, 65, 155–188 (1979)
    • Serre, J.-P.: Abelian l-adic representations and elliptic curves, New York. Benjamin, W. A (1968)
    • Shin, S.W.: On the cohomological base change for unitary similitude groups, Appendix to W. Goldring, Galois representations associated to...
    • Skinner, C.: A note on the p-adic Galois representations attached to Hilbert modular forms. Doc. Math. 14, 241–258 (2009)
    • The Stacks project authors: The Stacks project, https://stacks.math.columbia.edu (2020)
    • Tits, J.: Représentations linéaires irréductibles d’un groupe réductif sur un corps quelconque. Journal für die reine und angewandte Mathematik...
    • Tung, S.-N.: On the automorphy of 2-dimensional potentially semi-stable deformation rings of GQp. Algebra Number Theory 15(9), 2173–2194 (2021)
    • Tung, S.-N.: On the modularity of 2-adic potentially semi-stable deformation rings. Math. Z. 298(1–2), 107–159 (2021)
    • Vogan, D.A., Jr.: The local Langlands correspondence. Contemp. Math. 145, 305–379 (1993)
    • Wallach, N.R.: Real reductive groups. I, Pure and Applied Mathematics, 132, (1988)
    • Zhu, Xinwen: A note on integral Satake isomorphisms, Preprint (2020), arXiv:2005.13056
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno