375 research outputs found

    Some uniform bounds for elliptic curves over Q\mathbb Q

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    We give explicit uniform bounds for several quantities relevant to the study of Galois representations attached to elliptic curves E/QE/\mathbb Q. We consider in particular the subgroup of scalars in the image of Galois, the first Galois cohomology group with values in the torsion of EE, and the Kummer extensions generated by points of infinite order in E(Q)E(\mathbb Q).Comment: Comments are welcome

    Effective Kummer Theory for Elliptic Curves

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    Let EE be an elliptic curve defined over a number field KK, let alphainE(K)alpha in E(K) be a point of infinite order, and let N1alphaN^{-1}alpha be the set of NN-division points of alphaalpha in E(overlineK)E(overline{K}). We prove strong effective and uniform results for the degrees of the Kummer extensions [K(E[N],N1alpha):K(E[N])][K(E[N],N^{-1}alpha) : K(E[N])]. When K=mathbbQK=mathbb Q, and under a minimal (necessary) assumption on alphaalpha, we show that the inequality [mathbbQ(E[N],N1alpha):mathbbQ(E[N])]geqcN2[mathbb Q(E[N],N^{-1}alpha) : mathbb Q(E[N])] geq cN^2 holds for a positive constant cc independent of both EE and alphaalpha

    Division in modules and Kummer theory

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    In this work we generalize the concept of injective module and develop a theory of divisibility for modules over a general ring, which provides a general and unified framework to study Kummer-like field extensions arising from commutative algebraic groups. With these tools we provide an effective bound for the degree of the field extensions arising from division points of elliptic curves, extending previous results of Javan Peykar for CM curves and of Lombardo and the author for the non-CM case

    Kummer theory for commutative algebraic groups

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    This thesis consists of four research articles that treat different aspects of Kummer theory for commutative algebraic groups, with particular emphasis on explicit and effective results

    Sebastiano Moruzzi, Vaghezza. Confini, cumuli e paradossi, Laterza, Bari 2012, pp. 196

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    The text offers a Critical Review of "Vaghezza. Confini, cumuli e paradossi" by Sebastiano Moruzzi. The author critically reflects on the book by considering its methodologies, its arguments, and its relation with other books of the same type and on the same subject.Il testo propone una Lettura Critica del libro "Vaghezza. Confini, cumuli e paradossi" di Sebastiano Moruzzi. L'autrice riflette criticamente sul libro considerandone le metodologie, gli argomenti e il nesso con altri libri dello stesso tipo e sullo stesso argomento

    Client-consultant interaction practices: Sources of ingenuity, value creation and strategizing

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    Service providers increasingly choose to interact with their clients. Previous studies show that client’s resources and activities can influence the service provider’s ability to create value, to be creative, and to develop competitive strategies. Yet several gaps can be identified in the literature regarding how these abilities are impacted by client-consultant interaction (c-c-i) practices. The purpose of this doctoral thesis is to explain the service providers’ varying ability to offer highly valuable solutions to their clients’ problems, in terms of the practices through which consultants interact with their clients. The main research questions are; How do client-consultant interaction practices influence a firm’s ability to offer unique value propositions and deliver ingenious solutions, and how do these practices influence the formation of the firm’s strategy? These questions are answered through four papers. Each paper answers a sub-question. Paper 1 focuses on the impact of c-c-i practices on the service providers’ ingenuity capabilities. The paper asks how project teams shatter constraints in ill-structured problem-solving situations, and what implications this finding has for the understanding of creative action in organizations. This paper sheds light on the c-c-i practices through which project teams shatter their constraints and create ingenious solutions. Paper 2 focuses on the creative aspects of c-c-i practices and presents the experiences of service providers who have been successful in capitalizing on the creative resources provided by their clients. Paper 3 is an inquiry into the relationship between c-c-i practices and the service providers’ ability to offer unique value propositions. The paper provides a model to define and assess value created through c-c-i practices. The findings of this paper show that value creation is maximized through c-c-i practices that provide access to various forms of capital and practice that enable capital exploitation. Unique value offerings can be developed from knowing what c-c-i practices to enact in different circumstances. Paper 4 focuses on the implications of c-c-i practices for the emergence of new strategies. The findings show that mundane business operations can be the locus of strategizing, and that clients can play a role in emergent strategy formation. Theoretical resources for this research are drawn from literature on practice theory, strategy, organizational creativity, and value creation. An explorative research design is used and qualitative data are gathered from 30 cases through extensive field work. Both in-depth and comparative case analyses are performed

    Client-consultant interaction practices: Sources of ingenuity, value creation and strategizing

    No full text
    Service providers increasingly choose to interact with their clients. Previous studies show that client’s resources and activities can influence the service provider’s ability to create value, to be creative, and to develop competitive strategies. Yet several gaps can be identified in the literature regarding how these abilities are impacted by client-consultant interaction (c-c-i) practices. The purpose of this doctoral thesis is to explain the service providers’ varying ability to offer highly valuable solutions to their clients’ problems, in terms of the practices through which consultants interact with their clients. The main research questions are; How do client-consultant interaction practices influence a firm’s ability to offer unique value propositions and deliver ingenious solutions, and how do these practices influence the formation of the firm’s strategy? These questions are answered through four papers. Each paper answers a sub-question. Paper 1 focuses on the impact of c-c-i practices on the service providers’ ingenuity capabilities. The paper asks how project teams shatter constraints in ill-structured problem-solving situations, and what implications this finding has for the understanding of creative action in organizations. This paper sheds light on the c-c-i practices through which project teams shatter their constraints and create ingenious solutions. Paper 2 focuses on the creative aspects of c-c-i practices and presents the experiences of service providers who have been successful in capitalizing on the creative resources provided by their clients. Paper 3 is an inquiry into the relationship between c-c-i practices and the service providers’ ability to offer unique value propositions. The paper provides a model to define and assess value created through c-c-i practices. The findings of this paper show that value creation is maximized through c-c-i practices that provide access to various forms of capital and practice that enable capital exploitation. Unique value offerings can be developed from knowing what c-c-i practices to enact in different circumstances. Paper 4 focuses on the implications of c-c-i practices for the emergence of new strategies. The findings show that mundane business operations can be the locus of strategizing, and that clients can play a role in emergent strategy formation. Theoretical resources for this research are drawn from literature on practice theory, strategy, organizational creativity, and value creation. An explorative research design is used and qualitative data are gathered from 30 cases through extensive field work. Both in-depth and comparative case analyses are performed

    Radical entanglement for elliptic curves

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    Let GG be a commutative connected algebraic group over a number field KK, let AA be a finitely generated and torsion-free subgroup of G(K)G(K) of rank r>0r>0 and, for n>1n>1, let K(n1A)K(n^{-1}A) be the smallest extension of KK inside an algebraic closure K\overline K over which all the points PG(K)P\in G(\overline K) such that nPAnP\in A are defined. We denote by ss the unique non-negative integer such that G(K)[n](Z/nZ)sG(\overline K)[n]\cong (\mathbb Z/n\mathbb Z)^s for all n1n\geq 1. We prove that, under certain conditions, the ratio between nrsn^{rs} and the degree [K(n1A):K(G[n])][K(n^{-1}A):K(G[n])] is bounded independently of n>1n>1 by a constant that depends only on the \ell-adic Galois representations associated with GG and on some arithmetic properties of AA as a subgroup of G(K)G(K) modulo torsion. In particular we extend the main theorems of [13] about elliptic curves to the case of arbitrary rank

    A 3V 15b 157W Cryo-CMOS DAC for Multiplexed Spin-Qubit Biasing

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    This paper presents a 15b cryo-CMOS DAC for multiplexed spin-qubit biasing implemented in a 22-nm FinFET process. The integrating-DAC architecture and the robust digitally-assisted high-voltage output stage enable a low power dissipation (157W) and small area (0.08mm2) independent of the number of biased qubits, and a 3V output range well beyond the nominal supply. This represents the first scalable solution for cryo-CMOS qubit biasing, which achieves a 1.8× better voltage resolution with a lower DNL over a 3× larger output range than the current state-of-the-art. Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.QCD/Sebastiano LabElectronicsQuantum Circuit Architectures and Technolog

    Ripensare l'Abruzzo. Novità su Sebastiano di Cola da Casentino

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    Negli ultimi anni la pittura e la scultura abruzzese del Rinascimento sono state oggetto di attenzione da parte della storiografia artistica ma tra gli artisti meno studiati che forse vale la pena approfondire è sicuramente Sebastiano di Cola da Casentino, pittore e scultore legato per via documentaria a Silvestro dell’Aquila e a Saturnino Gatti che si può inserire tra i protagonisti più interessanti della scuola aquilana della seconda metà del Quattrocento. Il suo nome si tramanda perché l’artista è firmatario dell’affresco a Santa Maria ad Cryptas a Fossa e di una Madonna in terracotta policroma e conservata ora presso il deposito di San Gregorio Magno ad Ascoli Piceno ma proveniente da Arquata del Tronto. Dalle sue prime opere l’artista mostra stretti legami stilistici con la cultura romana coeva e in particolare con Antoniazzo Romano, Melozzo da Forlì e gli artisti della Cappella Sistina. Dai confronti documentari e stilistici delle opere a lui riferibili si può tracciare il profilo di un artista che con la sua bottega si era inserito perfettamente della vita artistica aquilana capace di realizzare opere di grande interesse, come si è cercato di evidenziare nel corso di questo contributo. Sebbene la sua figura sia stata in passato sottovalutata, il maestro in realtà ha delle potenzialità che vengono approfondite, migliorate e aggiornate sulla cultura contemporanea. Sebastiano è una figura attiva e si muove dall’Aquila, come fanno altri artisti contemporanei e partecipa a questo aggiornamento in senso rinascimentale della cultura aquilana tra la fine del Quattrocento e primi anni del XVI secolo non solo con la diffusione del linguaggio verrocchiesco che viene attraverso Firenze ma anche tramite un rapporto strettissimo con la Roma di Antoniazzo Romano, di Melozzo da Forlì e di tutti quegli artisti attivi nel cantiere sistino
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