Factorisation de la cohomologie étale p-adique de la tour de Drinfeld
Forum of Mathematics, Pi, Tome 11 (2023)

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Pierre Colmez; Gabriel Dospinescu; Wiesława Nizioł. Factorisation de la cohomologie étale p-adique de la tour de Drinfeld. Forum of Mathematics, Pi, Tome 11 (2023). doi: 10.1017/fmp.2023.15

[1] Ardakov, K., Wadsley, S., Irreducibility of global sections of Drinfeld line bundles, en préparation.Google Scholar

[2] Barthel, L., Livné, R., Irreducible modular representations of of a local field, Duke Math. J. 75 (1994), 261–292.Google Scholar | DOI

[3] Barthel, L., Livné, R., Modular representations of of a local field: the ordinary, unramified case, J. Number Theory 55 (1995), 1–27.Google Scholar | DOI

[4] Berger, L., Central characters for smooth irreducible modular representations of , Rend. Semin. Mat. Univ. Padova 128 (2012), 1–6.Google Scholar | DOI

[5] Berger, L., Représentations modulaires de et représentations galoisiennes de dimension , Astérisque 330 (2010), 263–279.Google Scholar

[6] Berger, L., Colmez, P., Familles de représentations de de Rham et monodromie -adique, Astérisque 319 (2008), 303–337.Google Scholar

[7] Berkovich, V., Vanishing cycles for formal schemes, Invent. math. 115 (1994), 539–571.Google Scholar | DOI

[8] Berkovich, V., Complex analytic vanishing cycles for formal schemes, preprint.Google Scholar

[9] Bloch, S., Kato, K., -adic étale cohomology, Publ. IHES 63 (1986), 107–152.Google Scholar | DOI

[10] Borel, A., Wallach, N., Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Math. Studies 94, Princeton University Press, 1980.Google Scholar

[11] Breuil, C., Sur quelques représentations modulaires et -adiques de . I, Compositio Math. 138 (2003), 165–188.Google Scholar | DOI

[12] Breuil, C., Paškūnas, V., Towards a modulo Langlands correspondence for , Memoirs of Amer. Math. Soc. 216, 2012.Google Scholar | DOI

[13] Caraiani, A., Emerton, M., Gee, T., Geraghty, D., Paškūnas, V., Shin, S. W., Patching and the -adic local Langlands correspondence, Cambridge J. Math. 4 (2016), 197–287.Google Scholar | DOI

[14] Colmez, P., Représentations de et -modules, Astérisque 330 (2010), 281–509.Google Scholar

[15] Colmez, P., Dospinescu, G., Complétés universels de représentations de , Algebra and Number Theory 8 (2014), 1447–1519.Google Scholar | DOI

[16] Colmez, P., Dospinescu, G., Nizioł, W., Cohomologie -adique de la tour de Drinfeld: le cas de la dimension , J. AMS 33 (2020), 311–362.Google Scholar

[17] Colmez, P., Dospinescu, G., Nizioł, W., Cohomology of -adic Stein spaces, Invent. math. 219 (2020), 873–985.Google Scholar | DOI

[18] Colmez, P., Dospinescu, G., Nizioł, W., Cohomologie des courbes analytiques -adiques, Cambridge J. Math. 10 (2022), 511–655.Google Scholar | DOI

[19] Colmez, P., Dospinescu, G., Nizioł, W., Correspondance de Langlands locale -adique et anneaux de Kisin, Acta Arithmetica (à paraître).Google Scholar

[20] Colmez, P., Dospinescu, G., Paškūnas, V., The -adic local Langlands correspondence for , Cambridge J. Math. 2 (2014), 1–47.Google Scholar | DOI

[21] Colmez, P., Fontaine, J.-M., Construction des représentations -adiques semi-stables, Invent. math. 140 (2000), 1–43.Google Scholar | DOI

[22] De Jong, A. J., Van Der Put, M., Étale cohomology of rigid analytic spaces , Doc. Math. 1 (1996), 1–56.Google Scholar | DOI

[23] Dospinescu, G., Le Bras, A.-C., Revêtements du demi-plan de Drinfeld et correspondance de Langlands -adique, Annals of Math. 186 (2017), 321–411.Google Scholar | DOI

[24] Dospinescu, G., Schraen, B., Endomorphism algebras of admissible -adic representations of -adic Lie groups, Representation Theory 17 (2013), 237–246.Google Scholar | DOI

[25] Dospinescu, G., Schraen, B., Paškūnas, V., Gelfand-Kirillov dimension and the -adic Jacquet-Langlands correspondence, J. reine angew. Math. (à paraître).Google Scholar

[26] Dotto, A., Emerton, M., Gee, T., Localization of smooth -power torsion representations of , [math.NT].Google Scholar | arXiv

[27] Drinfeld, V., Coverings of -adic symmetric regions, Funktsional. Anal. i Prilozhen., (1976), 29-40; Funct. Anal. Appl., (1976), 107-115.Google Scholar

[28] Emerton, M., Local-global compatibility in the -adic Langlands programme for , preprint 2009!Google Scholar

[29] Emerton, M., Ordinary parts of admissible representations of -adic reductive groups I. Definition and first properties, Astérisque 331 (2010), 335–381.Google Scholar

[30] Emerton, M., Ordinary parts of admissible representations of -adic reductive groups II. The relation to parabolic induction, Astérisque 331 (2010), 383–438.Google Scholar

[31] Faltings, G., A relation between two moduli spaces studied by V.G.Drinfeld, In: Algebraic number theory and algebraic geometry, Contemp. Math. 300 (2002), 115–129.Google Scholar | DOI

[32] Fontaine, J.-M., Messing, W., -adic periods and -adic étale cohomology, In: Current Trends in Arithmetical Algebraic Geometry, Contemporary Math. 67 (1987), 179–207.Google Scholar | DOI

[33] Fontaine, J.-M., Représentations -adiques potentiellement semi-stables, Astérisque 223 (1994), 321–347.Google Scholar

[34] Fust, P., Continuous Cohomology and Ext-Groups, Münster J. Math. 15 (2022), 279–304.Google Scholar

[35] Gabriel, P., Des catégories abéliennes , Bull. SMF 90 (1962), 323–448.Google Scholar

[36] Gee, T., Kisin, M., The Breuil-Mézard conjecture for potentially Barsotti-Tate representations, Forum of Mathematics Pi 2 (2014), 56 pp.Google Scholar | DOI

[37] Glöckner, H., Lectures on Lie groups over local fields , In: New directions in locally compact groups, 37–72, London Math. Soc. Lecture Note Ser., 447, Cambridge Univ. Press, 2018.Google Scholar | DOI

[38] Gross, B., Hopkins, M., Equivariant vector bundles on the Lubin-Tate space, In: Topology and representation theory (Evanston, IL, 1992), Contemp. Math. 158 (1994), 23–88.Google Scholar

[39] Hauseux, J., Extensions entre séries principales -adiques et modulo de , J. Inst. Math. Jussieu 15 (2016), 225–270.Google Scholar | DOI

[40] Hu, Y., Diagrammes canoniques et représentations modulo de , J. Inst. Math. Jussieu 11 (2012), 67–118.Google Scholar | DOI

[41] Hu, Y., Wang, H., On the mod cohomology for : the non-semisimple case, Cambridge J. Math. 10 (2022), 261–431.Google Scholar | DOI

[42] Hu, Y., Wang, H., On some mod representations of quaternion algebra over , [math.NT]Google Scholar | arXiv

[43] Huber, R., Étale cohomology of rigid analytic varieties and adic spaces, Aspects of Mathematics E30, Vieweg & Sohn, 1996.Google Scholar | DOI

[44] Hyodo, O., A note on -adic étale cohomology in the semistable reduction case, Invent. math. 91 (1988), 543–557.Google Scholar | DOI

[45] Kedlaya, K., Sheaves, stacks, and shtukas, In: Perfectoid spaces. Lectures from the 2017 Arizona Winter School, held in Tucson, AZ, March 11–17, Mathematical Surveys and Monographs , American Mathematical Society, 2019.Google Scholar

[46] Kisin, M., Potentially semi-stable deformation rings , J. AMS 21 (2008), 513–546.Google Scholar

[47] Kohlhaase, J., Smooth duality in natural characteristic , Adv. Math. 317 (2017), 1–49.Google Scholar | DOI

[48] Le, D., On some nonadmissible smooth irreducible representations for , Math. Res. Lett. 26 (2019), 1747–1758.Google Scholar | DOI

[49] Ludwig, J., A quotient of the Lubin-Tate tower , Forum Math. Sigma 5 (2017), e17.Google Scholar | DOI

[50] Moore, C., Group extensions of -adic and adelic linear groups, Publ. IHES 35 (1968), 157–222.Google Scholar | DOI

[51] Nakajima, S., On Galois module structure of the cohomology groups of an algebraic variety , Invent. math. 75 (1984), 1–8.Google Scholar | DOI

[52] Paškūnas, V., Extensions for supersingular representations of ) , Astérisque 331 (2010), 317–353.Google Scholar

[53] Paškūnas, V., The image of Colmez’s Montreal functor , Publ. IHES 118 (2013), 1–191.Google Scholar | DOI

[54] Paškūnas, V., Blocks for mod representations of , In: Automorphic forms and Galois representations. Vol. 2, 231–247, London Math. Soc. Lecture Note Ser. , Cambridge Univ. Press, 2014.Google Scholar | DOI

[55] Paškūnas, V., On some consequences of a theorem of J. Ludwig, J. Inst. Math. Jussieu 21 (2022), 1067–1106.Google Scholar | DOI

[56] Paškūnas, V., Tung, S.-N., Finiteness properties of the category of mod representations of , Forum Math. Sigma 9 (2021), e80, 39 pp.Google Scholar | DOI

[57] Patel, D., Schmidt, T., Strauch, M., Locally analytic representations of via semistable models of , J. Inst. Math. Jussieu 18 (2019), 125–187.Google Scholar | DOI

[58] Porter, T., Essential properties of pro-objects in Grothendieck categories , Cah. Topol. Géom. Différ. Catég. 20 (1979), 3–57.Google Scholar

[59] Rozensztajn, S., On the locus of -dimensional crystalline representations with a given reduction modulo , Algebra & Number Theory 14 (2020), 643–700.Google Scholar | DOI

[60] Scholze, P., -adic Hodge theory for rigid-analytic varieties, Forum Math. Pi 1 (2013), 77 pp.Google Scholar | DOI

[61] Scholze, P., On the -adic cohomology of the Lubin-Tate tower, Ann. ENS 51 (2018), 811–863.Google Scholar

[62] Scholze, P., Étale cohomology of diamonds, [math.AG].Google Scholar | arXiv

[63] Scholze, P., Weinstein, J., Moduli of -divisible groups, Cambridge J. Math. 1 (2013), 145–237.Google Scholar | DOI

[64] Schneider, P., Nonarchimedean Functional Analysis, Springer Monographs in Mathematics, Springer-Verlag 2002.Google Scholar | DOI

[65] Schneider, P., Teitelbaum, J., Algebras of -adic distributions and admissible representations, Invent. math. 153 (2003), 145–196.Google Scholar | DOI

[66] Schraen, B., Sur la présentation des représentations supersingulières de , J. Reine Angew. Math. 704 (2015), 187–208.Google Scholar | DOI

[67] Shotton, J., The category of finitely presented smooth mod  representations of , Doc. Math. 25 (2020), 143–157.Google Scholar | DOI

[68] Strauch, M., Geometrically connected components of of Lubin-Tate deformation spaces with level structures, Pure and Applied Mathematics Q. 4 (2008), 1215–1232 Google Scholar | DOI

[69] Tsuji, T., -adic étale cohomology and crystalline cohomology in the semi-stable reduction case, Invent. math. 137 (1999), 233–411.Google Scholar | DOI

[70] Vignéras, M.-F., Le foncteur de Colmez pour , In: Arithmetic geometry and automorphic forms, Adv. Lect. Math. (ALM), vol. 19, Int. Press, 2011, pp. 531–557.Google Scholar

[71] Wu, Z., A note on presentations of supersingular representations of , Manuscripta Math. 165 (2021), 583–596.Google Scholar | DOI

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