Tate conjecture for a product of a Shimura curve and a Picard modular surface
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- by Cristian Virdol PDF
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Abstract:
In this paper we prove the Tate conjecture for a product of a Shimura curve and a Picard modular surface.References
- T. Barnet-Lamb, T. Gee, D. Geraghty, R. Taylor, Potential automorphy and change of weight, preprint.
- Tom Barnet-Lamb, David Geraghty, Michael Harris, and Richard Taylor, A family of Calabi-Yau varieties and potential automorphy II, Publ. Res. Inst. Math. Sci. 47 (2011), no. 1, 29–98. MR 2827723, DOI 10.2977/PRIMS/31
- Don Blasius and Jonathan D. Rogawski, Tate classes and arithmetic quotients of the two-ball, The zeta functions of Picard modular surfaces, Univ. Montréal, Montreal, QC, 1992, pp. 421–444. MR 1155236
- Charles W. Curtis and Irving Reiner, Methods of representation theory. Vol. I, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1981. With applications to finite groups and orders. MR 632548
- Pierre Deligne, Travaux de Shimura, Séminaire Bourbaki, 23ème année (1970/71), Exp. No. 389, Lecture Notes in Math., Vol. 244, Springer, Berlin, 1971, pp. 123–165 (French). MR 0498581
- B. Brent Gordon, Canonical models of Picard modular surfaces, The zeta functions of Picard modular surfaces, Univ. Montréal, Montreal, QC, 1992, pp. 1–29. MR 1155224
- G. Harder, R. P. Langlands, and M. Rapoport, Algebraische Zyklen auf Hilbert-Blumenthal-Flächen, J. Reine Angew. Math. 366 (1986), 53–120 (German). MR 833013
- Robert P. Langlands, Base change for $\textrm {GL}(2)$, Annals of Mathematics Studies, No. 96, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 574808
- Robert P. Langlands and Dinakar Ramakrishnan (eds.), The zeta functions of Picard modular surfaces, Université de Montréal, Centre de Recherches Mathématiques, Montreal, QC, 1992. MR 1155223
- Jonathan D. Rogawski, Analytic expression for the number of points mod $p$, The zeta functions of Picard modular surfaces, Univ. Montréal, Montreal, QC, 1992, pp. 65–109. MR 1155227
- J. D. Rogawski and J. B. Tunnell, On Artin $L$-functions associated to Hilbert modular forms of weight one, Invent. Math. 74 (1983), no. 1, 1–42. MR 722724, DOI 10.1007/BF01388529
- John T. Tate, Algebraic cycles and poles of zeta functions, Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963) Harper & Row, New York, 1965, pp. 93–110. MR 0225778
- John Tate, Conjectures on algebraic cycles in $l$-adic cohomology, Motives (Seattle, WA, 1991) Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 71–83. MR 1265523, DOI 10.1090/pspum/055.1/1265523
- Richard Taylor, On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989), no. 2, 265–280. MR 1016264, DOI 10.1007/BF01388853
Additional Information
- Cristian Virdol
- Affiliation: Department of Mathematics, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
- Address at time of publication: Department of Mathematics, Room 208, Yonsei University, Seoul 120-749, South Korea
- MR Author ID: 781239
- Email: virdol@yonsei.ac.kr
- Received by editor(s): February 5, 2011
- Received by editor(s) in revised form: April 15, 2012
- Published electronically: December 6, 2013
- Communicated by: Matthew A. Papanikolas
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 827-834
- MSC (2010): Primary 11F41, 11F80, 11R42, 11R80
- DOI: https://doi.org/10.1090/S0002-9939-2013-11819-8
- MathSciNet review: 3148517