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Vanishing of the μ-invariant of p-adic Hecke L-functions

Part of: Arithmetic algebraic geometry Algebraic number theory: global fields Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  24 March 2011

Haruzo Hida
Haruzo Hida*
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA (email: [email protected])
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Abstract

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We prove vanishing of the μ-invariant of the p-adic Katz L-function in N. M. Katz [p-adic L-functions for CM fields, Invent. Math. 49 (1978), 199–297].

Keywords

Iwasawa invariantHecke L-functionHilbert modular varietyEisenstein seriesShimura variety

MSC classification

Secondary: 11R23: Iwasawa theory 11F33: Congruences for modular and $p$-adic modular forms 11F41: Automorphic forms on $(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11F60: Hecke-Petersson operators, differential operators (several variables) 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11G18: Arithmetic aspects of modular and Shimura varieties
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 4 , July 2011 , pp. 1151 - 1178
Copyright
Copyright © Foundation Compositio Mathematica 2011

References

[Cha90]Chai, C.-L., Arithmetic minimal compactification of the Hilbert–Blumenthal moduli spaces, Ann. of Math. (2) 131 (1990), 541–554.Google Scholar
[Del71]Deligne, P., Travaux de Shimura, Séminaire Bourbaki, Exposé 389, Lecture Notes in Mathematics, vol. 244 (Springer, Berlin, 1971), 123–165.Google Scholar
[Del79]Deligne, P., Variétés de Shimura: interprétation modulaire, et techniques de construction de modéles canoniques, Proc. Sympos. Pure Math. 33 (1979), 247–290.CrossRefGoogle Scholar
[DR80]Deligne, P. and Ribet, K. A., Values of abelian L-functions at negative integers over totally real fields, Invent. Math. 59 (1980), 227–286.Google Scholar
[Gil91]Gillard, R., Remarques sur l’invariant mu d’Iwasawa dans le cas CM, Sémin. Théor. Nombres Bordeaux, Sér. II 3 (1991), 13–26.CrossRefGoogle Scholar
[Hid04]Hida, H., p-adic automorphic forms on Shimura varieties, Springer Monographs in Mathematics (Springer, Berlin, 2004) (a list of errata available at http://www.math.ucla.edu/∼hida ).CrossRefGoogle Scholar
[Hid09]Hida, H., Irreducibility of the Igusa tower, Acta Math. Sin. (Engl. Ser.) 25 (2009), 1–20.CrossRefGoogle Scholar
[Hid10]Hida, H., The Iwasawa μ-invariant of p-adic Hecke L-functions, Ann. of Math. (2) 172 (2010), 41–137.Google Scholar
[HT93]Hida, H. and Tilouine, J., Anticyclotomic Katz p-adic L-functions and congruence modules, Ann. Sci. Éc. Norm. Supér. (4) 26 (1993), 189–259.Google Scholar
[Kat78a]Katz, N. M., p-adic L-functions for CM fields, Invent. Math. 49 (1978), 199–297.CrossRefGoogle Scholar
[Kat78b]Katz, N. M., Serre–Tate local moduli, in Surfaces algébriques, Lecture Notes in Mathematics, vol. 868 (Springer, Berlin, 1978), 138–202.Google Scholar
[Kot92]Kottwitz, R., Points on Shimura varieties over finite fields, J. Amer. Math. Soc. 5 (1992), 373–444.Google Scholar
[Mum94]Mumford, D., Abelian varieties, TIFR Studies in Mathematics (Oxford University Press, Oxford, 1994).Google Scholar
[Shi66]Shimura, G., Moduli and fibre system of abelian varieties, Ann. of Math. (2) 83 (1966), 294–338.Google Scholar
[Shi75]Shimura, G., On some arithmetic properties of modular forms of one and several variables, Ann. of Math. (2) 102 (1975), 491–515.Google Scholar
[Shi98]Shimura, G., Abelian varieties with complex multiplication and modular functions (Princeton University Press, Princeton, 1998).CrossRefGoogle Scholar
[Shi00]Shimura, G., Arithmeticity in the theory of automorphic forms, Mathematical Surveys and Monographs, vol. 82 (American Mathematical Society, Providence, RI, 2000).Google Scholar