Contents
Research Article
On arithmetic families of filtered
$\varphi $-modules and crystalline representations
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- Published online by Cambridge University Press: 19 September 2012, pp. 677-726
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We consider stacks of filtered
$\varphi $-modules over rigid analytic spaces and adic spaces. We show that these modules parameterize 
$p$-adic Galois representations of the absolute Galois group of a 
$p$-adic field with varying coefficients over an open substack containing all classical points. Further, we study a period morphism (defined by Pappas and Rapoport) from a stack parameterizing integral data, and determine the image of this morphism.
Hybrid bounds for automorphic forms on ellipsoids over number fields
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- Published online by Cambridge University Press: 20 December 2012, pp. 727-758
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We prove upper bounds for Hecke–Laplace eigenfunctions on certain Riemannian manifolds
$X$ of arithmetic type, uniformly in the eigenvalue and the volume of the manifold. The manifolds under consideration are 
$d$-fold products of 
$2$-spheres or 
$3$-spheres, realized as adelic quotients of quaternion algebras over totally real number fields. In the volume aspect we prove a (‘Weyl-type’) saving of 
$\mathrm{vol} \hspace{0.167em} (X)^{- 1/ 6+ \varepsilon } $.
Sur la conjecture de Manin pour certaines surfaces de Châtelet
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- Published online by Cambridge University Press: 08 March 2013, pp. 759-819
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Nous démontrons, sous la forme forte conjecturée par Peyre, la conjecture de Manin pour les surfaces de Châtelet dont les équations sont du type
${y}^{2} + {z}^{2} = P(x, 1)$, où 
$P$ est une forme binaire quartique à coefficients entiers irréductible sur 
$ \mathbb{Q} [i] $ ou produit de deux formes quadratiques à coefficients entiers irréductibles sur 
$ \mathbb{Q} [i] $. De plus, nous fournissons une estimation explicite du terme d’erreur de la formule asymptotique sous-jacente. Cela finalise essentiellement la validation de la conjecture de Manin pour l’ensemble des surfaces de Châtelet. La preuve s’appuie sur deux méthodes nouvelles, concernant, du part, les estimations en moyenne d’oscillations locales de caractères sur les diviseurs, et, d’autre part, les majorations de certaines fonctions arithmétiques de formes binaires.
Des points fixes communs pour des difféomorphismes de
${ \mathbb{S} }^{2} $ qui commutent et préservent une mesure de probabilité
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- Published online by Cambridge University Press: 08 February 2013, pp. 821-851
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Nous montrons des résultats d’existence de points fixes communs pour des homéomorphismes du plan
${ \mathbb{R} }^{2} $ ou la sphère 
${ \mathbb{S} }^{2} $, qui commutent deux à deux et préservent une mesure de probabilité. Par exemple, nous montrons que des 
${C}^{1} $-difféomorphismes 
${f}_{1} , \ldots , {f}_{n} $ de 
${ \mathbb{S} }^{2} $ suffisamment proches de l’identité, qui commutent deux à deux, et qui préservent une mesure de probabilité dont le support n’est pas réduit à un point, ont au moins deux points fixes communs.
Failure of the Hasse principle on general
$K 3$ surfaces
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- Published online by Cambridge University Press: 08 February 2013, pp. 853-877
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We show that transcendental elements of the Brauer group of an algebraic surface can obstruct the Hasse principle. We construct a general
$K 3$ surface 
$X$ of degree 
$2$ over 
$ \mathbb{Q} $, together with a 2-torsion Brauer class 
$\alpha $ that is unramified at every finite prime, but ramifies at real points of 
$X$. With motivation from Hodge theory, the pair 
$(X, \alpha )$ is constructed from a double cover of 
${ \mathbb{P} }^{2} \times { \mathbb{P} }^{2} $ ramified over a hypersurface of bidegree 
$(2, 2)$.
De Branges’ theorem on approximation problems of Bernstein type
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- Published online by Cambridge University Press: 27 February 2013, pp. 879-899
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The Bernstein approximation problem is to determine whether or not the space of all polynomials is dense in a given weighted
${C}_{0} $-space on the real line. A theorem of de Branges characterizes non-density by existence of an entire function of Krein class being related with the weight in a certain way. An analogous result holds true for weighted sup-norm approximation by entire functions of exponential type at most 
$\tau $ and bounded on the real axis (
$\tau \gt 0$ fixed).We consider approximation in weighted
${C}_{0} $-spaces by functions belonging to a prescribed subspace of entire functions which is solely assumed to be invariant under division of zeros and passing from 
$F(z)$ to 
$ \overline{F( \overline{z} )} $, and establish the precise analogue of de Branges’ theorem. For the proof we follow the lines of de Branges’ original proof, and employ some results of Pitt.
Front Cover (OFC, IFC) and matter
JMJ volume 12 issue 4 Cover and Front matter
- Published online by Cambridge University Press: 27 August 2013, pp. f1-f2
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Back Cover (IBC, OBC) and matter
JMJ volume 12 issue 4 Cover and Back matter
- Published online by Cambridge University Press: 27 August 2013, pp. b1-b2
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