Serre weights for U⁢(n)

References

[1] A. Ash, D. Doud and D. Pollack, Galois representations with conjectural connections to arithmetic cohomology, Duke Math. J. 112 (2002), no. 3, 521–579. 10.1215/S0012-9074-02-11235-6Suche in Google Scholar

[2] T. Barnet-Lamb, T. Gee, D. Geraghty and R. Taylor, Local-global compatibility for l=p. II, Ann. Sci. Éc. Norm. Supér. (4) 47 (2014), no. 1, 161–175. 10.24033/asens.2212Suche in Google Scholar

[3] T. Barnet-Lamb, T. Gee, D. Geraghty and R. Taylor, Potential automorphy and change of weight, Ann. of Math. (2) 179 (2014), no. 2, 501–609. 10.4007/annals.2014.179.2.3Suche in Google Scholar

[4] T. Barnet-Lamb, T. Gee and D. Geraghty, The Sato–Tate conjecture for Hilbert modular forms, J. Amer. Math. Soc. 24 (2011), no. 2, 411–469. 10.1090/S0894-0347-2010-00689-3Suche in Google Scholar

[5] T. Barnet-Lamb, T. Gee and D. Geraghty, Congruences between Hilbert modular forms: Constructing ordinary lifts, Duke Math. J. 161 (2012), no. 8, 1521–1580. 10.1215/00127094-1593326Suche in Google Scholar

[6] 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

[7] J. Bellaïche and G. Chenevier, The sign of Galois representations attached to automorphic forms for unitary groups, Compos. Math. 147 (2011), no. 5, 1337–1352. 10.1112/S0010437X11005264Suche in Google Scholar

[8] A. Caraiani, Local-global compatibility and the action of monodromy on nearby cycles, Duke Math. J. 161 (2012), no. 12, 2311–2413. 10.1215/00127094-1723706Suche in Google Scholar

[9] A. Caraiani, Monodromy and local-global compatibility for l=p, Algebra Number Theory 8 (2014), no. 7, 1597–1646. 10.2140/ant.2014.8.1597Suche in Google Scholar

[10] G. Chenevier and M. Harris, Construction of automorphic Galois representations. II, Camb. J. Math. 1 (2013), 57–74. 10.4310/CJM.2013.v1.n1.a2Suche in Google Scholar

[11] L. Clozel, M. Harris and R. Taylor, Automorphy for some l-adic lifts of automorphic mod l Galois representations, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 1–181. 10.1007/s10240-008-0016-1Suche in Google Scholar

[12] M. Emerton, T. Gee and F. Herzig, Weight cycling and Serre-type conjectures for unitary groups, Duke Math. J. 162 (2013), no. 9, 1649–1722. 10.1215/00127094-2266365Suche in Google Scholar

[13] M. Emerton, T. Gee, F. Herzig and D. Savitt, Explicit Serre weight conjectures, in preparation. Suche in Google Scholar

[14] H. Gao and T. Liu, A note on potential diagonalizability of crystalline representations, Math. Ann. 360 (2014), no. 1–2, 481–487. 10.1007/s00208-014-1041-7Suche in Google Scholar

[15] T. Gee, A modularity lifting theorem for weight two Hilbert modular forms, Math. Res. Lett. 13 (2006), no. 5–6, 805–811. 10.4310/MRL.2006.v13.n5.a10Suche in Google Scholar

[16] T. Gee, Automorphic lifts of prescribed types, Math. Ann. 350 (2011), no. 1, 107–144. 10.1007/s00208-010-0545-zSuche in Google Scholar

[17] T. Gee and D. Geraghty, Companion forms for unitary and symplectic groups, Duke Math. J. 161 (2012), no. 2, 247–303. 10.1215/00127094-1507376Suche in Google Scholar

[18] T. Gee, T. Liu and D. Savitt, The weight part of Serre’s conjecture for GL⁡(2), Forum Math. Pi 3 (2015), Article ID e2. 10.1017/fmp.2015.1Suche in Google Scholar

[19] 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

[20] T. Gee and D. Savitt, Serre weights for mod p Hilbert modular forms: The totally ramified case, J. reine angew. Math. 660 (2011), 1–26. 10.1515/crelle.2011.079Suche in Google Scholar

[21] R. Guralnick, F. Herzig, R. Taylor and J. Thorne, Adequate subgroups, appendix to: On the automorphy of l-adic Galois representations with small residual image, J. Inst. Math. Jussieu 11 (2012), no. 4, 855–920. 10.1017/S1474748012000023Suche in Google Scholar

[22] M. Harris and R. Taylor, The geometry and cohomology of some simple Shimura varieties, Ann. of Math. Stud. 151, Princeton University Press, Princeton 2001. 10.1515/9781400837205Suche in Google Scholar

[23] F. Herzig, The weight in a Serre-type conjecture for tame n-dimensional Galois representations, Duke Math. J. 149 (2009), no. 1, 37–116. 10.1215/00127094-2009-036Suche in Google Scholar

[24] J. C. Jantzen, Representations of algebraic groups, 2nd ed., Math. Surveys Monogr. 107, American Mathematical Society, Providence 2003. Suche in Google Scholar

[25] M. Kisin, Potentially semi-stable deformation rings, J. Amer. Math. Soc. 21 (2008), no. 2, 513–546. 10.1090/S0894-0347-07-00576-0Suche in Google Scholar

[26] 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

[27] J.-P. Labesse, Changement de base CM et séries discrètes, Stabilization of the trace formula, Shimura varieties, and arithmetic applications. Volume 1: On the stabilization of the trace formula, International Press, Somerville (2011), 429–470. Suche in Google Scholar

[28] S. W. Shin, Galois representations arising from some compact Shimura varieties, Ann. of Math. (2) 173 (2011), no. 3, 1645–1741. 10.4007/annals.2011.173.3.9Suche in Google Scholar

[29] R. Taylor and T. Yoshida, Compatibility of local and global Langlands correspondences, J. Amer. Math. Soc. 20 (2007), no. 2, 467–493 (electronic). 10.1090/S0894-0347-06-00542-XSuche in Google Scholar

[30] J. Thorne, On the automorphy of l-adic Galois representations with small residual image, J. Inst. Math. Jussieu 11 (2012), no. 4, 855–920. 10.1017/S1474748012000023Suche in Google Scholar

[31] S. Wortmann, Galois representations of three-dimensional orthogonal motives, Manuscripta Math. 109 (2002), no. 1, 1–28. 10.1007/s002290200287Suche in Google Scholar