Links between generalized Montr\'eal-functors

Let $o$ be the ring of integers in a finite extension $K/\mathbb{Q}_p$ and $G=\mathbf{G}(\mathbb{Q}_p)$ be the $\mathbb{Q}_p$-points of a $\mathbb{Q}_p$-split reductive group $\mathbf{G}$ defined over $\mathbb{Z}_p$ with connected centre and split Borel $\mathbf{B}=\mathbf{TN}$. We show that Breuil's pseudocompact $(\varphi,\Gamma)$-module $D^\vee_{\xi}(\pi)$ attached to a smooth $o$-torsion representation $\pi$ of $B=\mathbf{B}(\mathbb{Q}_p)$ is isomorphic to the pseudocompact completion of the basechange $\mathcal{O_E}\otimes_{\Lambda(N_0),\ell}\widetilde{D_{SV}}(\pi)$ to Fontaine's ring (via a Whittaker functional $\ell\colon N_0=\mathbf{N}(\mathbb{Z}_p)\to \mathbb{Z}_p$) of the \'etale hull $\widetilde{D_{SV}}(\pi)$ of $D_{SV}(\pi)$ defined by Schneider and Vigneras. Moreover, we construct a $G$-equivariant map from the Pontryagin dual $\pi^\vee$ to the global sections $\mathfrak{Y}(G/B)$ of the $G$-equivariant sheaf $\mathfrak{Y}$ on $G/B$ attached to a noncommutative multivariable version $D^\vee_{\xi,\ell,\infty}(\pi)$ of Breuil's $D^\vee_{\xi}(\pi)$ whenever $\pi$ comes as the restriction to $B$ of a smooth, admissible representation of $G$ of finite length.Comment: 50 pp, revise

Spin-dominated waveforms for unequal mass compact binaries

We derive spin-dominated waveforms (SDW) for binary systems composed of spinning black holes with unequal masses (less than 1:30). Such systems could be formed by an astrophysical black hole with a smaller black hole or a neutron star companion; and typically arise for supermassive black hole encounters. SDW characterize the last stages of the inspiral, when the larger spin dominates over the orbital angular momentum (while the spin of the smaller companion can be neglected). They emerge as a double expansion in the post-Newtonian parameter $\varepsilon$ and the ratio $\xi$ of the orbital angular momentum and dominant spin. The SDW amplitudes are presented to ($\varepsilon^{3/2},\xi$) orders, while the phase of the gravitational waves to ($\varepsilon^{2},\xi$) orders (omitting the highest order mixed terms). To this accuracy the amplitude includes the (leading order) spin-orbit contributions, while the phase the (leading order) spin-orbit, self-spin and mass quadrupole-monopole contributions. While the SDW hold for any mass ratio smaller than 1:30, lower bounds for the mass ratios are derived from the best sensitivity frequency range expected for Advanced LIGO (giving 1:140), the Einstein Telescope ($7\times 10^{-4}$), the LAGRANGE ($7\times 10^{-7}$) and LISA missions ($7\times 10^{-9}$), respectively.Comment: 14 pages, 2 figures, 5 tables, published versio

Credit Growth in Central and Eastern Europe: Convergence or Boom?

Credit to the private sector has been growing very rapidly in a number of Central and Eastern European countries in recent years. The main question is whether this dynamics is an equilibrium convergence process or may rather pose stability risks. Using panel econometric techniques, this paper attempts to identify the equilibrium credit/GDP levels of the new EU countries, disentangling the observed growth into an equilibrium trend and an excess (boom) component. In the paper the pooled mean group estimator was used for its flexibility and efficiency. Using instrumental variable technique we tested whether long run endogeneity affects the consistency. The estimations show that large part of the credit growth in new member states can be explained by the catching-up process, and, in general, credit/GDP ratios are below the levels consistent with macroeconomic fundamentals. However, in Latvia and Estonia credit growth is found to be significantly faster than what would be justified along the equilibrium path.financial deepening, credit growth, transition economies, panel econometrics, endogeneity bias.