Hecke fields of analytic families of modular forms

DOI10.1090/S0894-0347-2010-00680-7zbMath1282.11058MaRDI QIDQ3074552

Haruzo Hida

Publication date: 9 February 2011

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Galois representationWeil numberanalytic familyHecke field

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) (p)-adic theory, local fields (11F85) Holomorphic modular forms of integral weight (11F11) Galois representations (11F80) General binary quadratic forms (11E16)

Related Items (10)

A finiteness property of abelian varieties with potentially ordinary good reduction ⋮ Growth of Hecke Fields Along a p-Adic Analytic Family of Modular Forms ⋮ Unlikely intersections on the \(p\)-adic formal ball ⋮ Classical forms of weight one in ordinary families ⋮ Constancy of adjoint \(\mathcal L\)-invariant ⋮ On fields of rationality for automorphic representations ⋮ \(p\)-adic properties of motivic fundamental lines ⋮ Transcendence of Hecke operators in the big Hecke algebra ⋮ EXCEPTIONAL ZEROES OF P-ADIC L-FUNCTIONS OVER NON-ABELIAN FIELD EXTENSIONS ⋮ Big Galois representations and -adic -functions

Cites Work

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• Motives for modular forms
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• Isogeny classes of abelian varieties over finite fields
• Arithmetic Moduli of Elliptic Curves. (AM-108)
• on l-adic representations attached to modular forms II
• Iwasawa modules attached to congruences of cusp forms
• Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert
• On two problems of E. M. Robinson about sums of roots of unity
• Adjoint Selmer groups as Iwasawa modules
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