Abstract
Let
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1751281
Award Identifier / Grant number: DMS-1952556
Funding source: National Security Agency
Award Identifier / Grant number: H98230-21-1-0029
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: EXC-2047/1 – 390685813
Funding source: Engineering and Physical Sciences Research Council
Award Identifier / Grant number: EP/W001683/1
Funding statement: This work began at the APAW Collaborative Research workshop supported by Ellen Eischen’s NSF CAREER grant DMS-1751281 and her NSA MSP conference grant H98230-21-1-0029. The work was completed at the trimester program “The Arithmetic of the Langlands Program” at the Hausdorff Institute for Mathematics, funded by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy – EXC-2047/1 – 390685813. B. Levin was supported by National Science Foundation grant DMS-1952556 and the Alfred P. Sloan Foundation. D. Savitt was supported by NSF grant DMS-1952566. H. Wiersema was supported by the Herchel Smith Postdoctoral Fellowship Fund, and the Engineering and Physical Sciences Research Council (EPSRC) grant EP/W001683/1.
Acknowledgements
This project began at the APAW Collaborative Research Workshop at the University of Oregon in August 2022 and was completed during various visits by six of us to the trimester program “The Arithmetic of the Langlands Program” at the Hausdorff Institute for Mathematics. We are grateful to Ellen Eischen, Maria Fox, Cathy Hsu, and Aaron Pollack for organizing the workshop, and we thank Frank Calegari, Ana Caraiani, Laurent Fargues, and Peter Scholze for their efforts organizing the trimester. We thank Matthew Emerton and Toby Gee for valuable conversations.
References
[1] T. Barnet-Lamb, T. Gee and D. Geraghty, Serre weights for rank two unitary groups, Math. Ann. 356 (2013), no. 4, 1551–1598. 10.1007/s00208-012-0893-ySuche in Google Scholar
[2] R. Bartlett, Inertial and Hodge–Tate weights of crystalline representations, Math. Ann. 376 (2020), no. 1–2, 645–681. 10.1007/s00208-019-01931-3Suche in Google Scholar
[3] C. Breuil, Integral 𝑝-adic Hodge theory, Algebraic Geometry 2000, Adv. Stud. Pure Math. 36, Mathematical Society of Japan, Tokyo (2002), 51–80. 10.2969/aspm/03610051Suche in Google Scholar
[4]
C. Breuil,
Sur un problème de compatibilité local-global modulo 𝑝 pour
[5]
C. Breuil and A. Mézard,
Multiplicités modulaires et représentations de
[6] K. Buzzard, F. Diamond and F. Jarvis, On Serre’s conjecture for mod ℓ Galois representations over totally real fields, Duke Math. J. 155 (2010), no. 1, 105–161. 10.1215/00127094-2010-052Suche in Google Scholar
[7] A. Caraiani, M. Emerton, T. Gee and D. Savitt, Local geometry of moduli stacks of two-dimensional Galois representations, Arithmetic Geometry 2020, TIFR Stud. Math. 24, Tata Institute of Fundamental Research Publications, Mumbai (2024), 127–202. Suche in Google Scholar
[8] A. Caraiani, M. Emerton, T. Gee and D. Savitt, The geometric Breuil–Mézard conjecture for two-dimensional potentially Barsotti–Tate Galois representions, preprint (2022), https://arxiv.org/abs/2207.05235; to appear in Algebra Number Theory. Suche in Google Scholar
[9] A. Caraiani, M. Emerton, T. Gee and D. Savitt, Components of moduli stacks of two-dimensional Galois representations, Forum Math. Sigma 12 (2024), Paper No. e31. 10.1017/fms.2024.4Suche in Google Scholar
[10] X. Caruso, A. David and A. Mézard, Un calcul d’anneaux de déformations potentiellement Barsotti–Tate, Trans. Amer. Math. Soc. 370 (2018), no. 9, 6041–6096. 10.1090/tran/6973Suche in Google Scholar
[11] F. Diamond and S. Sasaki, A Serre weight conjecture for geometric Hilbert modular forms in characteristic 𝑝, J. Eur. Math. Soc. (JEMS) 25 (2023), no. 9, 3453–3536. 10.4171/jems/1265Suche in Google Scholar
[12] M. Emerton, Formal algebraic stacks, http://www.math.uchicago.edu/~emerton/pdffiles/formal-stacks.pdf. Suche in Google Scholar
[13] M. Emerton and T. Gee, ‘Scheme-theoretic images’ of morphisms of stacks, Algebr. Geom. 8 (2021), no. 1, 1–132. 10.14231/AG-2021-001Suche in Google Scholar
[14]
M. Emerton and T. Gee,
Moduli sacks of étale (
[15] M. Emerton, T. Gee and E. Hellmann, An introduction to the categorical 𝑝-adic Langlands program, preprint (2022), https://arxiv.org/abs/2210.01404. Suche in Google Scholar
[16] T. Gee and M. Kisin, The Breuil–Mézard conjecture for potentially Barsotti–Tate representations, Forum Math. Pi 2 (2014), Paper No. e1. 10.1017/fmp.2014.1Suche in Google Scholar
[17] T. Gee, T. Liu and D. Savitt, The Buzzard–Diamond–Jarvis conjecture for unitary groups, J. Amer. Math. Soc. 27 (2014), no. 2, 389–435. 10.1090/S0894-0347-2013-00775-4Suche in Google Scholar
[18]
T. Gee, T. Liu and D. Savitt,
The weight part of Serre’s conjecture for
[19] M. Kisin, Moduli of finite flat group schemes, and modularity, Ann. of Math. (2) 170 (2009), no. 3, 1085–1180. 10.4007/annals.2009.170.1085Suche in Google Scholar
[20] D. Le, B. V. Le Hung, B. Levin and S. Morra, Potentially crystalline deformation rings and Serre weight conjectures: Shapes and shadows, Invent. Math. 212 (2018), no. 1, 1–107. 10.1007/s00222-017-0762-0Suche in Google Scholar
[21] D. Le, B. V. Le Hung, B. Levin and S. Morra, Local models for Galois deformation rings and applications, Invent. Math. 231 (2023), no. 3, 1277–1488. 10.1007/s00222-022-01163-4Suche in Google Scholar
[22] R. Taylor and A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995), no. 3, 553–572. 10.2307/2118560Suche in Google Scholar
[23] H. Wiersema, Minimal weights of mod 𝑝 Galois representations, PhD thesis, King’s College London, 2021. Suche in Google Scholar
[24] A. Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443–551. 10.2307/2118559Suche in Google Scholar
[25] The Stacks project authors, The stacks project, http://stacks.math.columbia.edu,2018. Suche in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Inverse mean curvature flow and Ricci-pinched three-manifolds
- Irregular loci in the Emerton–Gee stack for GL2
- Stationary measures for SL2(ℝ)-actions on homogeneous bundles over flag varieties
- The Lichnerowicz Laplacian on normal homogeneous spaces
- Sharp pinching theorems for complete submanifolds in the sphere
- On Vafa–Witten equations over Kähler manifolds
- Sheaf quantization from exact WKB analysis
- Reduced resonance schemes and Chen ranks
- Eisenstein degeneration of Euler systems
- Erratum to Discriminants and Artin conductors (J. reine angew. Math. 712 (2016), 107–121)
Artikel in diesem Heft
- Frontmatter
- Inverse mean curvature flow and Ricci-pinched three-manifolds
- Irregular loci in the Emerton–Gee stack for GL2
- Stationary measures for SL2(ℝ)-actions on homogeneous bundles over flag varieties
- The Lichnerowicz Laplacian on normal homogeneous spaces
- Sharp pinching theorems for complete submanifolds in the sphere
- On Vafa–Witten equations over Kähler manifolds
- Sheaf quantization from exact WKB analysis
- Reduced resonance schemes and Chen ranks
- Eisenstein degeneration of Euler systems
- Erratum to Discriminants and Artin conductors (J. reine angew. Math. 712 (2016), 107–121)