7,823 research outputs found

    On the cuspidality of pullbacks of Siegel Eisenstein series and applications to the Bloch-Kato conjecture

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    Let k>3k > 3 be an integer and pp a prime with p>2k2p > 2k-2. Let ff be a newform of weight 2k22k-2 and level 1 so that ff is ordinary at pp and ρˉf\bar{\rho}_{f} is irreducible. Under some additional hypotheses we prove that ord_{p}(L_{alg}(k,f)) \leq ord_{p}(# S) where SS is the Pontryagin dual of the Selmer group associated to ρfϵ1k\rho_{f} \otimes \epsilon^{1-k} with ϵ\epsilon the pp-adic cyclotomic character. We accomplish this by first constructing a congruence between the Saito-Kurokawa lift of ff and a non-CAP Siegel cusp form. Once this congruence is established, we use Galois representations to obtain the lower bound on the Selmer group.Comment: 33 page

    Residually reducible representations of algebras over local Artinian rings

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    In this paper we generalize a result of Urban on the structure of residually reducible representations on local Artinian rings from the case that the semi-simplification of the residual representation splits into 2 absolutely irreducible representations to the case where it splits into m ≥ 2 absolutely irreducible representations

    A Call to Action: An Integrated Approach to Youth Permanency and Preparation for Adulthood

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    Addresses the unique needs of adolescents in foster care, and highlights efforts to ensure that youth in the foster system benefit from the most strategic preparation and supports for entering adulthood
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