Congruences among modular forms on U(2,2) and the Bloch-Kato conjecture
| dc.creator | Klosin, Krzysztof | |
| dc.date | 2007-10-12 | |
| dc.date.accessioned | 2026-07-07T08:36:11Z | |
| dc.date.available | 2026-07-07T08:36:11Z | |
| dc.description | Let 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.description | 57 pages | |
| dc.identifier | https://arxiv.org/abs/0710.2549 | |
| dc.identifier | http://arxiv.org/abs/0710.2549 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139980 | |
| dc.subject | Number Theory | |
| dc.subject | Representation Theory | |
| dc.subject | 11F33, 11F55, 11F67, 11F80 | |
| dc.title | Congruences among modular forms on U(2,2) and the Bloch-Kato conjecture | |
| dc.type | text |