A Cup Product in the Galois Cohomology of Number Fields

Let K be a number field containing the group of n-th roots of unity and S a set of primes of K including all those dividing n and all real archimedean places. We consider the cup product on the first Galois cohomology group of the maximal S-ramified extension of K with coefficients in n-th roots of unity, which yields a pairing on a subgroup of the multiplicative group of K containing the S-units. In this general situation, we determine a formula for the cup product of two elements which pair trivially at all local places. Our primary focus is the case that K is the cyclotomic field of p-th roots of unity for n = p an odd prime and S consists of the unique prime above p in K. We describe a formula for this cup product in the case that one element is a p-th root of unity. We explain a conjectural calculation of the restriction of the cup product to p-units for all p < 10,000 and conjecture its surjectivity for all p satisfying Vandiver's conjecture. We prove this for the smallest irregular prime p = 37, via a computation related to the Galois module structure of p-units in the unramified extension of K of degree p. We describe a number of applications: to a product map in K-theory, to the structure of S-class groups in Kummer extensions of K, to relations in the Galois group of the maximal pro-p extension of K unramified outside p, to relations in the graded Z_p-Lie algebra associated to the representation of the absolute Galois group of Q in the outer automorphism group of the pro-p fundamental group of P^1 minus three points, and to Greenberg's pseudo-nullity conjecture.Comment: final versio

Money Stock Control with Reserve and Interest Rate Instruments Under Rational Expectations

This paper conducts a theoretical comparison of the potential effectiveness, in terms of money stock controllability, of interest rate and reserve instruments. Whereas previous studies have been basically static, the present analysis is carried out in the context of a dynamic macroeconomic model with rational expectations. Particular attention is paid to the distinction between contemporaneous and lagged reserve accounting (CRA and LRA). The criterion employed is the expectation of squared deviations of the (log of the) money stock from target values that are reset each period. Analysis in the basic model suggests the following substantive conclusions. (1) With a reserve instrument, monetary control will be more effective under CRA than LRA. (2) With a reserve instrument and LRA, control will be poorer than with an interest rate instrument. (3) For a wide range of parameter values, control will be better with a reserve instrument and CRA than with an interest rate instrument.

The effect of low-energy ion-implantation on the electrical transport properties of Si-SiO2 MOSFETs

Using silicon MOSFETs with thin (5nm) thermally grown SiO2 gate dielectrics, we characterize the density of electrically active traps at low-temperature after 16keV phosphorus ion-implantation through the oxide. We find that, after rapid thermal annealing at 1000oC for 5 seconds, each implanted P ion contributes an additional 0.08 plus/minus 0.03 electrically active traps, whilst no increase in the number of traps is seen for comparable silicon implants. This result shows that the additional traps are ionized P donors, and not damage due to the implantation process. We also find, using the room temperature threshold voltage shift, that the electrical activation of donors at an implant density of 2x10^12 cm^-2 is ~100%.Comment: 11 pages, 10 figure

High superconducting anisotropy and weak vortex pinning in Co doped LaFeAsO

Here, we present an electrical transport study in single crystals of LaFe$_{0.92}$Co$_{0.08}$AsO ($T_c \simeq 9.1$ K) under high magnetic fields. In contrast to most of the previously reported Fe based superconductors, and despite its relatively low $T_c$, LaFe$_{1-x}$Co$_x$AsO shows a superconducting anisotropy which is comparable to those seen for instance in the cuprates or $\gamma_H = H_{c2}^{ab}/H_{c2}^{c} = m_c/m_{ab} \simeq 9$, where $m_c/m_{ab}$ is the effective mass anisotropy. Although, in the present case and as in all Fe based superconductors, $\gamma \rightarrow 1$ as $T \rightarrow 0$. Under the application of an external field, we also observe a remarkable broadening of the superconducting transition particularly for fields applied along the inter-planar direction. Both observations indicate that the low dimensionality of LaFe$_{1-x}$Co$_x$AsO is likely to lead to a more complex vortex phase-diagram when compared to the other Fe arsenides and consequently, to a pronounced dissipation associated with the movement of vortices in a possible vortex liquid phase. When compared to, for instance, F-doped compounds pertaining to same family, we obtain rather small activation energies for the motion of vortices. This suggests that the disorder introduced by doping LaFeAsO with F is more effective in pinning the vortices than alloying it with Co.Comment: 7 figures, 7 pages, Phys. Rev. B (in press

New results on heavy hadron spectroscopy with NRQCD

We present results for the spectrum of b-bbar bound states in the quenched approximation for three different values of the lattice spacing. Results for spin-independent splittings are shown to have good scaling behaviour; spin-dependent splittings are more sensitive to discretisation effects. We discuss what needs to be done to match the experimental spectrum.Comment: 3 pages, contribution to Lattice'9