- Précédent

- Feuilleter

- Série 6 : Tome 33 (2024)

- no. 4

- p. 1155-1213

- Résumé (VO)

- Abstract

Inspiré par le travail de Pan, on définit et étudie un foncteur qui associe à des faisceaux équivariants sur la droite projective des faisceaux automorphes sur les courbes modulaires. Ce point de vue nous permet d’utiliser des techniques de théorie des représentations pour étudier les vecteurs localement analytiques dans la cohomologie complétée ainsi que sa structure de Hodge–Tate.

Inspired by the work of Pan, we define and study a functor which attaches to equivariant sheaves on the projective line automorphic sheaves on modular curves. This point of view allows us to use representation theory techniques in the study of the locally analytic vectors in completed cohomology and its Hodge–Tate structure.

- Détail

- Export

- Comment citer

Vincent Pilloni 1

- BibTeX

- RIS

- EndNote

- Bibliographie

- Cité par

[1] Fabrizio Andreatta; Adrian Iovita; Glenn Stevens Overconvergent modular sheaves and modular forms for GL 2/F , Isr. J. Math., Volume 201 (2014) no. 1, pp. 299-359 | Zbl | DOI | MR

[2] Alexander Beĭlinson; Joseph Bernstein A generalization of Casselman’s submodule theorem, Representation theory of reductive groups (Park City, Utah, 1982) (Progress in Mathematics), Volume 40, Birkhäuser, 1983, pp. 35-52 | DOI | Zbl | MR

[3] Laurent Berger; Pierre Colmez Familles de représentations de de Rham et monodromie p-adique, Représentations p-adiques de groupes p-adiques. I. Représentations galoisiennes et (ϕ,Γ)-modules (Astérisque), Volume 319, Société Mathématique de France, 2008, pp. 303-337 | Numdam | MR | Zbl

[4] Laurent Berger; Pierre Colmez Théorie de Sen et vecteurs localement analytiques, Ann. Sci. Éc. Norm. Supér., Volume 49 (2016) no. 4, pp. 947-970 | Numdam | Zbl | DOI | MR

[5] George Boxer; Vincent Pilloni Higher Hida and Coleman theories on the modular curves (2020) | arXiv

[6] Przemysł aw Chojecki; David Hansen; Christian Johansson Overconvergent modular forms and perfectoid Shimura curves, Doc. Math., Volume 22 (2017), pp. 191-262 | DOI | Zbl | MR

[7] Robert F. Coleman Classical and overconvergent modular forms, Invent. Math., Volume 124 (1996) no. 1-3, pp. 215-241 | Zbl | DOI | MR

[8] Hansheng Diao; Kai-Wen Lan; Ruochuan Liu; Xinwen Zhu Logarithmic Riemann-Hilbert correspondences for rigid varieties (2019) | arXiv

[9] Renée Elkik Solutions d’équations à coefficients dans un anneau hensélien, Ann. Sci. Éc. Norm. Supér., Volume 6 (1973), pp. 553-603 | DOI | Numdam | Zbl | MR

[10] Matthew Emerton On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms, Invent. Math., Volume 164 (2006) no. 1, pp. 1-84 | Zbl | DOI | MR

[11] Gerd Faltings Hodge-Tate structures and modular forms, Math. Ann., Volume 278 (1987) no. 1-4, pp. 133-149 | Zbl | DOI | MR

[12] Alexander Grothendieck Sur quelques points d’algèbre homologique, Tôhoku Math. J., Volume 9 (1957), pp. 119-221 | Zbl | DOI | MR

[13] Roland Huber A generalization of formal schemes and rigid analytic varieties, Math. Z., Volume 217 (1994) no. 4, pp. 513-551 | Zbl | DOI | MR

[14] James E. Humphreys Representations of semisimple Lie algebras in the BGG category 𝒪, Graduate Studies in Mathematics, 94, American Mathematical Society, 2008, xvi+289 pages | DOI | MR

[15] Jens Carsten Jantzen Representations of algebraic groups, Mathematical Surveys and Monographs, 107, American Mathematical Society, 2003, xiv+576 pages | MR

[16] Moritz Kerz; Shuji Saito; Georg Tamme Towards a non-archimedean analytic analog of the Bass-Quillen conjecture, J. Inst. Math. Jussieu, Volume 19 (2020) no. 6, pp. 1931-1946 | Zbl | DOI | MR

[17] Lue Pan On locally analytic vectors of the completed cohomology of modular curves, Forum Math. Pi, Volume 10 (2022), e7, 82 pages | Zbl | DOI | MR

[18] Vincent Pilloni Overconvergent modular forms, Ann. Inst. Fourier, Volume 63 (2013) no. 1, pp. 219-239 | Numdam | Zbl | DOI | MR

[19] J. E. Rodríguez Camargo Locally analytic completed cohomology (2022) | arXiv

[20] Peter Scholze Perfectoid spaces, Publ. Math., Inst. Hautes Étud. Sci., Volume 116 (2012), pp. 245-313 | Numdam | Zbl | DOI | MR

[21] Peter Scholze p-adic Hodge theory for rigid-analytic varieties, Forum Math. Pi, Volume 1 (2013), e1, 77 pages | Zbl | DOI | MR

[22] Peter Scholze On torsion in the cohomology of locally symmetric varieties, Ann. Math., Volume 182 (2015) no. 3, pp. 945-1066 | Zbl | DOI | MR

[23] The Stacks Project Authors Stacks Project, http://stacks.math.columbia.edu, 2013

Cité par Sources :