Hecke fields of analytic families of modular forms

Hida, Haruzo

doi:10.1090/S0894-0347-2010-00680-7

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ISSN 1088-6834(online) ISSN 0894-0347(print)

Hecke fields of analytic families of modular forms

Author: Haruzo Hida
Journal: J. Amer. Math. Soc. 24 (2011), 51-80
MSC (2010): Primary 11E16, 11F11, 11F25, 11F27, 11F30, 11F33, 11F80
Published electronically: September 8, 2010
MathSciNet review: 2726599
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Abstract: We make finiteness conjectures on the composite of Hecke fields of classical members of a -adic analytic family of slope 0 elliptic modular forms in the vertical case (with fixed level varying weight). In the horizontal case (fixed weight varying -power level), we prove the corresponding statements.

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