Congruences among modular forms on U(2,2) and the Bloch-Kato conjecture

dc.creatorKlosin, Krzysztof
dc.date2007-10-12
dc.date.accessioned2026-07-07T08:36:11Z
dc.date.available2026-07-07T08:36:11Z
dc.descriptionLet k be a positive integer divisible by 4, l>k a prime, and f an elliptic cuspidal eigenform of weight k-1, level 4, and non-trivial character. Let ρ_f be the l-adic Galois representation attached to f. In this paper we provide evidence for the Bloch-Kato conjecture for a twist of the adjoint motif of ρ_f in the following way. Let L(f,s) denote the symmetric square L-function of f. We prove that (under certain conditions) the l-adic valuation of the algebraic part of L(f, k) is no greater than the l-adic valuation of the order of S, where S is (the Pontryagin dual of) the Selmer group attached to the Galois module \ad^0ρ_f|_{G_K} (-1), and K= Q(i). Our method uses an idea of Ribet in that we introduce an intermediate step and produce congruences between CAP and non-CAP modular forms on the unitary group U(2,2).
dc.description57 pages
dc.identifierhttps://arxiv.org/abs/0710.2549
dc.identifierhttp://arxiv.org/abs/0710.2549
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139980
dc.subjectNumber Theory
dc.subjectRepresentation Theory
dc.subject11F33, 11F55, 11F67, 11F80
dc.titleCongruences among modular forms on U(2,2) and the Bloch-Kato conjecture
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