8,584 research outputs found

    Finite quotients of Z[C_n]-lattices and Tamagawa numbers of semistable abelian varieties

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    We investigate the behaviour of Tamagawa numbers of semistable principally polarised abelian varieties in extensions of local fields. In view of the Raynaud parametrisation, this translates into a purely algebraic problem concerning the number of HH-invariant points on a quotient of CnC_n-lattices Λ/eΛ′\Lambda/e\Lambda' for varying subgroups HH of CnC_n and integers ee. In particular, we give a simple formula for the change of Tamagawa numbers in totally ramified extensions (corresponding to varying ee) and one that computes Tamagawa numbers up to rational squares in general extensions. As an application, we extend some of the existing results on the pp-parity conjecture for Selmer groups of abelian varieties by allowing more general local behaviour. We also give a complete classification of the behaviour of Tamagawa numbers for semistable 2-dimensional principally polarised abelian varieties, that is similar to the well-known one for elliptic curves. The appendix explains how to use this classification for Jacobians of genus 2 hyperelliptic curves given by equations of the form y2=f(x)y^2=f(x), under some simplifying hypotheses.Comment: Two new lemmas are added. The first describes permutation representations, and the second describes the dependence of the B-group on the maximal fixpoint-free invariant sublattice. Contact details and bibliographic details have been update

    Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction

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    We study how Tamagawa numbers of Jacobians of hyperelliptic curves vary as one varies the base field or the curve, in the case of semistable reduction. We find that there are strong constraints on the behaviour that appears, some of which are unexpected and specific to hyperelliptic curves. Our methods are explicit and allow one to write down formulae for Tamagawa numbers of infinite families of hyperelliptic curves, of the kind used in proofs of the parity conjecture for Jacobians of curves of small genus

    Parental rearing style as a predictor of attachment and psychosocial adjustment during young adulthood

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    Parental rearing-styles are crucial for psychosocial adjustment both during childhood and adulthood. The current study examined whether: (a) parental rearing-styles predicted psychosocial adjustment in young-adulthood, (b) this relationship was mediated by attachment styles , and ( c ) gender differences occur in these relationships. Two hundred and forty (103 male and 132 female) university students completed measures assessing parental rearing-style , current attachment style, romantic relationship satisfaction, friendship quality, self-esteem, and social competence. Multigroup structural equation modelling, conducted separately by gender, revealed that parental rearing-style predicted psychosocial adjustment during young-adulthood. Further, there was also evidence of gender differences and that self-models and other-models of attachment mediated this relationship. Together, these findings reinforce the importance of perceived parental rearing-style for subsequent psychosocial adjustment

    Telemedicine in pediatric speech therapy: characteristics of child, mother, and speech-language pathologist vocal interaction.

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    Telemedicine is a potential solution to provide distant or underserved clients with access to their clinician. The purpose of this thesis is to examine how the use of telemedicine affects the vocal characteristics of children who received cochlear implants (CI), their mother, and a speech-language pathologist (SLP) as they engage in a speech-language therapy intervention. The children (n = 5), her caregiver, and the SLP engaged in one 30 minute in person session and one 30 minute telemedicine session in a counterbalanced order. The frequency of vocalizations, vocal turns, and between-speaker pause (BSP) duration in both sessions were examined. The results indicate that the SLP produced fewer vocalizations whereas the mother produced more vocalizations in the telemedicine compared to the in-person session. Additionally, there were fewer turns between the SLP and child and more turns between the mother and child in the telemedicine than the in-person sessions. The number of turns between the SLP and the mother and the occurrence of simultaneous speech were not affected by session type Finally, BSP duration was longer during telemedicine than the in-person session during SLP-Child and ChildSLP, Child-Mother turns. These results indicate that the vocal interaction between child, caregiver, and clinician are impacted by the use of telemedicine
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