1,720,964 research outputs found
On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields
No full textIf E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional eigenspace relative to a fixed complex ring class character provided that the projection onto this eigenspace of a suitable Drinfeld-Heegner point is nonzero. This represents the analogue in the function field setting of a theorem for rational elliptic curves due to Bertolini and Darmon, and at the same time is a generalization of the main result proved by Brown in his monograph on Heegner modules. As in the number field case, our proof employs Kolyvagin-type arguments, and the cohomological machinery is started up by the control on the Galois structure of the torsion of E provided by classical results of Igusa in positive characteristic
The Rationality of Quaternionic Darmon Points Over Genus Fields of Real Quadratic Fields
Full text linkDarmon points on p-adic tori and Jacobians of Shimura curves over Q were introduced in joint articles with Rotger as generalizations of Darmon's Stark-Heegner points. In this article, we study the algebraicity over extensions of a real quadratic field K of the projections of Darmon points to elliptic curves, which coincide with the points on elliptic curves previously defined by M. Greenberg. More precisely, we prove that linear combinations of Darmon points on elliptic curves weighted by certain genus characters of K are rational over the predicted genus fields of K. This extends to an arbitrary quaternionic setting the main theorem on the rationality of Stark-Heegner points obtained by Bertolini and Darmon, and at the same time gives evidence for the rationality conjectures formulated in a joint paper with Rotger and by Greenberg in his article on Stark-Heegner points. In light of this result, quaternionic Darmon points represent the first instance of a systematic supply of points of Stark-Heegner type other than Darmon's original ones for which explicit rationality results are known. © 2013 The Author(s) 2013. Published by Oxford University Press. All rights reserved
Vanishing of special values and central derivatives in Hida families
Full text linkThe theme of this work is the study of the Nekovář-Selmer group H1f(K, †) attached to a twisted Hida family † of Galois representations and a quadratic number field K. The results that we obtain have the following shape: if a twisted L-function of a suitable modular form in the Hida family has order of vanishing r ≤ 1 at the central critical point then the rank of H1f(K, †) as a module over a certain local Hida-Hecke algebra is equal to r. Under the above assumption, we also show that infinitely many twisted L-functions of modular forms in the Hida family have the same order of vanishing at the central critical point. Our theorems extend to more general arithmetic situations results obtained by Howard when K is an imaginary quadratic field and all the primes dividing the tame level of the Hida family split in K
A note on Control Theorems for quaternionic Hida families of modular forms
Full text linkWe extend a result of Greenberg and Stevens on the interpolation of
modular symbols in Hida families to the context of non-split rational quaternion algebras.
Both the denite case and the indenite case are considered
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
On the vanishing of Selmer groups for elliptic curves over ring class field
Full text linkLet E/Q be an elliptic curve of conductor N without complex multiplication and let K be an imaginary quadratic field of discriminant D prime to N. Assume that the number of primes dividing N and inert in K is odd, and let H(c) be the ring class field of K of conductor c prime to ND with Galois group G(c) over K. Fix a complex character \chi of G(c). Our main result is that if L_K(E, \chi, 1) not equal 0 then Sel_p(E/H(c))\otimes W = 0 for all but finitely many primes p, where Sel_p(E/H(c)) is the p-Selmer group of E over H(c) and W is a suitable finite extension of Z_p containing the values of \chi. Our work extends results of Bertolini and Darmon to almost all non-ordinary primes p and also offers alternative proofs of a \chi-twisted version of the Birch and Swinnerton-Dyer conjecture for E over H(c) (Bertolini and Darmon) and of the vanishing of Sel_p(E/K) for almost all p (Kolyvagin) in the case of analytic rank zero
An irreducibility criterion for group representations with arithmetic applications
Full text linkWe prove a criterion for the irreducibility of an integral group representation \rho over the fraction field of a Noetherian domain R in terms of suitably defined reductions of \rho at prime ideals of R. As applications, we give irreducibility results for universal deformations of residual representations, with special attention to universal deformations of residual Galois representations associated with modular forms of weight at least 2
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