Four dimensional Galois representations

Weissauer, Rainer

Formes automorphes (II) - Le cas du groupe

G S p (4)

, Astérisque, no. 302 (2005), pp. 67-150.

MR Zbl | 3 citations dans Numdam

@incollection{AST_2005__302__67_0,
     author = {Weissauer, Rainer},
     title = {Four dimensional {Galois} representations},
     booktitle = {Formes automorphes (II) - Le cas du groupe $GSp(4)$},
     editor = {Tilouine Jacques and Carayol Henri and Harris Michael and Vign\'eras Marie-France},
     series = {Ast\'erisque},
     pages = {67--150},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {302},
     year = {2005},
     mrnumber = {2234860},
     zbl = {1097.11027},
     language = {en},
     url = {https://www.numdam.org/item/AST_2005__302__67_0/}
}

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Weissauer, Rainer. Four dimensional Galois representations, dans Formes automorphes (II) - Le cas du groupe $GSp(4)$, Astérisque, no. 302 (2005), pp. 67-150. https://www.numdam.org/item/AST_2005__302__67_0/

Bibliographie
Cité par

[BW] A. Borel & N. Wallach - Continuous cohomology, discrete subgroups, and representations of reductive groups, 2nd ed., Math. Surv., vol. 67, American Mathematical Society, 2000. | MR | Zbl

[CF] C. L. Chai & G. Faltings - Degeneration of Abelian Varieties, Springer, 1990. | MR | Zbl

[GMP] M. Goresky & R. Macpherson - Lefschetz numbers of Hecke correspondences, in The zeta functions of Picard modular surfaces (R.P. Langlands & D. Ramakrishnan, eds.), Les Publications CRM, 1992, p. 465-478. | MR | Zbl

[GMP2] M. Goresky & R. Macpherson, The topological trace formula, J. reine angew. Math. 560 (2003), p. 71-150. | MR | Zbl

[G] P. A. Griffiths - Some transcendental methods in the study of algebraic cycles, in Several complex variables, Maryland, Lect. Notes in Math., vol. 185, Springer, 1970, p. 1-47. | MR | Zbl

[HST] M. Harris, D. Soudry & R. Taylor - $ℓ$ -adic representations associated to modular forms over imaginary fields, I. Lifting to GSp(4, $ℚ$ ), Invent. Math. 112 (1993), p. 377-411. | DOI | EuDML | MR | Zbl

[He] G. Henniart - Représentations $ℓ$ -adiques abéliennes, in Séminaire de théorie des nombres, Paris 1980-81, Séminaire Delange-Pisot-Poitou, Birkhäuser, 1982. | Zbl

[HPS] R. Howe & I. I. Piatetski-Shapiro - Some examples of automorphic forms on ${Sp}_{4}$ , Duke Math. J. 50 (1983), no. 1. | DOI | MR | Zbl

[JL] H. Jaquet & R. P. Langlands - Automorphic Forms on $G L (2)$ , Lect. Notes in Math., vol. 114, Springer, 1970. | MR | Zbl

[KV] M. Kashiwara & M. Vergne - On the Segal-Shale-Weil representation and harmonic polynomials, Invent. Math. 44 (1978), p. 1-47. | DOI | EuDML | MR | Zbl

[K] R. Kottwitz - Shimura varieties and twisted orbital integrals, Math. Ann. 269 (1984), p. 287-300. | DOI | EuDML | MR | Zbl

[K2] R. Kottwitz, Shimura varieties and $λ$ -adic representations, in Ann Arbor Proceedings (L. Clozel & J.S. Milne, eds.), Perspectives of Mathematics, Academic Press, 1990, p. 161-209. | MR | Zbl

[KS] R. Kottwitz & D. Shelstad - Foundations of twisted endoscopy, Astérisque, vol. 255, Société Mathématique de France, 1999. | Numdam | MR | Zbl

[KRS] S. S. Kudla, S. Rallis & D. Soudry - On the degree $5 L$ -function for $S p (2)$ , Invent. Math. 107 (1992), p. 483-541. | DOI | EuDML | MR | Zbl

[LL] J.-P. Labesse & R. P. Langlands - $L$ -indistinguishability for $S l (2)$ , Canad. J. Math. XXXI (1979), no. 4, p. 726-785. | DOI | MR | Zbl

[Lau] G. Laumon - Fonctions zêtas des variétés de Siegel de dimension trois, this volume. | Numdam | Zbl

[MS] J. Milne & K. Y. Shih - Conjugates of Shimura varieties, in Hodge cycles, Motives, and Shimura varieties, Lect. Notes in Math., vol. 900, Springer, 1982, p. 280-357. | DOI | Zbl

[P] I. I. Piateskii-Shapiro - On the Saito-Kurokawa lifting, Invent. Math. 71 (1983), p. 309-338. | DOI | EuDML | MR | Zbl

[PS] I. I. Piateskii-Shapiro & D. Soudry - $ε$ -factors for $G S p_{4}$ , J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28, no. 3. | MR | Zbl

[Pr] T. Przebinda - The oscillator correspondence for the pair $O (2, 2), S p (2, ℝ)$ , Mem. Amer. Math. Soc, vol. 403, American Mathematical Society, 1989. | MR | Zbl

[Sh] F. Shahidi - A proof of the Langland's conjecture on Plancherel measures; Complementary series for $p$ -adic groups, Ann. of Math. (2) 132 (1990), p. 273-330. | DOI | MR | Zbl

[Sha] J. Shalika - The multiplicity one theorem for $G l (n)$ , Ann. of Math. (2) 100 (1974), p. 171-193. | DOI | MR | Zbl

[S2] D. Soudry - A uniqueness theorem for representations of $G S O (6)$ and the strong multiplicity one theorem for generic representations of $G S p (4)$ , Israel I. Math. 58 (1987), p. 257-287. | DOI | MR | Zbl

[S] D. Soudry, The CAP representations of $G S p (4)$ , J. reine angew. Math. 383 (1988), p. 97-108. | MR | Zbl

[T2] R. Taylor - Galois representations associated to Siegel modular forms of low weight, Duke Math. I. 63 (1991), no. 2. | MR | Zbl

[T] R. Taylor, On the $ℓ$ -adic cohomology of Siegel threefolds, Invent. Math. 114 (1993), p. 289-310. | DOI | EuDML | MR | Zbl

[V] M. F. Vigneras - Correspondance entre représentations automorphes de $G l (2)$ sur une extension quadratique de $G S p (4)$ sur $Q$ , conjecture locale de Langlands pour $G S p (4)$ , Contemporary Mathematics, vol. 53, American Mathematical Society, 1986. | DOI | MR | Zbl

[W] R. Weissauer - Preprints on the Ramanujan conjecture for $G S p (4)$ , http://www.mathi.uni-heidelberg.de/~weissaue/papers/ramanuge.dvi, 1993/95.

[W1] R. Weissauer, Endoscopy for $G S p (4)$ , preprint, http://www.mathi.uni-heidelberg.de/~weissaue/papers/endoscopy.ps, 1998.