Ordinary -adic Eisenstein series and -adic -functions for unitary groups
- [1] National Taiwan University Department of Mathematics Taipei (Taiwan)
Annales de l’institut Fourier (2011)
- Volume: 61, Issue: 3, page 987-1059
- ISSN: 0373-0956
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top- M. Bertolini, H. Darmon, Iwasawa’s main conjecture for elliptic curves over anticyclotomic -extensions, Ann. of Math. (2) 162 (2005), 1-64 Zbl1093.11037MR2178960
- Ching-Li Chai, Compactification of Siegel moduli schemes, 107 (1985), Cambridge University Press, Cambridge Zbl0578.14009MR853543
- Ching-Li Chai, Methods for -adic monodromy, J. Inst. Math. Jussieu 7 (2008), 247-268 Zbl1140.14019MR2400722
- John Coates, Motivic -adic -functions, -functions and arithmetic (Durham, 1989) 153 (1991), 141-172, Cambridge Univ. Press, Cambridge Zbl0725.11029MR1110392
- Gerd Faltings, Ching-Li Chai, Degeneration of abelian varieties, 22 (1990), Springer-Verlag, Berlin Zbl0744.14031MR1083353
- Stephen Gelbart, Ilya Piatetski-Shapiro, Stephen Rallis, Explicit constructions of automorphic -functions, 1254 (1987), Springer-Verlag, Berlin Zbl0612.10022MR892097
- Ralph Greenberg, Iwasawa theory and -adic deformations of motives, Motives (Seattle, WA, 1991) 55 (1994), 193-223, Amer. Math. Soc., Providence, RI Zbl0819.11046MR1265554
- A. Grothendieck, M. Demazure, Schémas en groupes. II: Groupes de type multiplicatif, et structure des schémas en groupes généraux, 152 (1962/1964), Springer-Verlag, Berlin Zbl0209.24201MR274459
- Michael Harris, Eisenstein series on Shimura varieties, Ann. of Math. (2) 119 (1984), 59-94 Zbl0589.10030MR736560
- Michael Harris, Jian-Shu Li, Christopher M. Skinner, -adic -functions for unitary Shimura varieties. I. Construction of the Eisenstein measure, Doc. Math. Extra Vol. (2006), 393-464 (electronic) Zbl1143.11019MR2290594
- Haruzo Hida, Elementary theory of -functions and Eisenstein series, 26 (1993), Cambridge University Press, Cambridge Zbl0942.11024MR1216135
- Haruzo Hida, Control theorems of coherent sheaves on Shimura varieties of PEL type, J. Inst. Math. Jussieu 1 (2002), 1-76 Zbl1039.11041MR1954939
- Haruzo Hida, -adic automorphic forms on Shimura varieties, (2004), Springer-Verlag, New York Zbl1055.11032MR2055355
- Haruzo Hida, J. Tilouine, Katz -adic -functions, congruence modules and deformation of Galois representations, -functions and arithmetic (Durham, 1989) 153 (1991), 271-293, Cambridge Univ. Press, Cambridge Zbl0739.11022MR1110397
- Nicholas M. Katz, -adic -functions for CM fields, Invent. Math. 49 (1978), 199-297 Zbl0417.12003MR513095
- R. Kottwitz, Points on some Shimura varieties over finite fields, Journal of AMS 5 (1992), 373-443 Zbl0796.14014MR1124982
- Jian-Shu Li, Nonvanishing theorems for the cohomology of certain arithmetic quotients, J. Reine Angew. Math. 428 (1992), 177-217 Zbl0749.11032MR1166512
- Barry Mazur, A. Wiles, Class fields of abelian extensions of , Invent. Math. 76 (1984), 179-330 Zbl0545.12005MR742853
- C. Mœglin, J.-L. Waldspurger, Spectral decomposition and Eisenstein series, 113 (1995), Cambridge University Press, Cambridge Zbl0846.11032MR1361168
- Kenneth A. Ribet, A modular construction of unramified -extensions of , Invent. Math. 34 (1976), 151-162 Zbl0338.12003MR419403
- Goro Shimura, Confluent hypergeometric functions on tube domains, Math. Ann. 260 (1982), 269-302 Zbl0502.10013MR669297
- Goro Shimura, Euler products and Eisenstein series, 93 (1997), published for the Conference Board of the Mathematical Sciences, Washington, DC Zbl0906.11020MR1450866
- Goro Shimura, Yutaka Taniyama, Complex multiplication of abelian varieties and its applications to number theory, 6 (1961), The Mathematical Society of Japan, Tokyo Zbl0112.03502MR125113
- Christopher Skinner, Towards Main Conjectures for Modular Forms, RIMS Kokyuroku 1468 (2006), 149-157 Zbl1179.11037MR2459294
- Christopher Skinner, Eric Urban, The Iwasawa main conjecture for , (Oct 2008) Zbl1301.11074
- J. Tilouine, Eric Urban, Several-variable -adic families of Siegel-Hilbert cusp eigensystems and their Galois representations, Ann. Sci. École Norm. Sup. (4) 32 (1999), 499-574 Zbl0991.11016MR1693583
- Eric Urban, Selmer groups and the Eisenstein-Klingen ideal, Duke Math. J. 106 (2001), 485-525 Zbl1061.11027MR1813234
- Eric Urban, Groupes de Selmer et Fonctions -adiques pour les Représentations Modulaires Adjointes, (2006)
- A. Wiles, The Iwasawa conjecture for totally real fields, Ann. of Math. (2) 131 (1990), 493-540 Zbl0719.11071MR1053488
- B. Zhang, Fourier-Jacobi Expansion of Eisenstein series on nonsplit unitary groups, (2007)