Potentially Good Reduction of Barsotti-Tate Groups

Let R be a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, K the fraction field of R. Suppose G is a Barsotti-Tate group (p-divisible group) defined over K which acquires good reduction over a finite extension K' of K. We prove that there exists a constant c which depends on the absolute ramification index e(K'/Q_p) and the height of G such that G has good reduction over K if and only if G[p^c] can be extended to a finite flat group scheme over R. For abelian varieties with potentially good reduction, this result generalizes Grothendieck's p-adic Neron-Ogg-Shafarevich criterion to finite level. We use methods that can be generalized to study semi-stable p-adic Galois representations with general Hodge-Tate weights, and in particular leads to a proof of a conjecture of Fontaine and gives a constant c as above that is independent of the height of G

The K\"ahler Potential of Abelian Higgs Vortices

We calculate the K\"ahler potential for the Samols metric on the moduli space of Abelian Higgs vortices on \mathbbm{R}^{2}, in two different ways. The first uses a scaling argument. The second is related to the Polyakov conjecture in Liouville field theory. The K\"ahler potential on the moduli space of vortices on \mathbbm{H}^{2} is also derived, and we are led to a geometrical reinterpretation of these vortices. Finally, we attempt to find the K\"ahler potential for vortices on \mathbbm{R}^{2} in a third way by relating the vortices to SU(2) Yang-Mills instantons on \mathbbm{R}^{2}\times S^{2}. This approach does not give the correct result, and we offer a possible explanation for this.Comment: 25 page

Self-reproduction in k-inflation

We study cosmological self-reproduction in models of inflation driven by a scalar field $\phi$ with a noncanonical kinetic term ($k$-inflation). We develop a general criterion for the existence of attractors and establish conditions selecting a class of $k$-inflation models that admit a unique attractor solution. We then consider quantum fluctuations on the attractor background. We show that the correlation length of the fluctuations is of order $c_{s}H^{-1}$, where $c_{s}$ is the speed of sound. By computing the magnitude of field fluctuations, we determine the coefficients of Fokker-Planck equations describing the probability distribution of the spatially averaged field $\phi$. The field fluctuations are generally large in the inflationary attractor regime; hence, eternal self-reproduction is a generic feature of $k$-inflation. This is established more formally by demonstrating the existence of stationary solutions of the relevant FP equations. We also show that there exists a (model-dependent) range $\phi_{R}<\phi<\phi_{\max}$ within which large fluctuations are likely to drive the field towards the upper boundary $\phi=\phi_{\max}$, where the semiclassical consideration breaks down. An exit from inflation into reheating without reaching $\phi_{\max}$ will occur almost surely (with probability 1) only if the initial value of $\phi$ is below $\phi_{R}$. In this way, strong self-reproduction effects constrain models of $k$-inflation.Comment: RevTeX 4, 17 pages, 1 figur

Intersecting branes from 7-manifolds with G_2 holonomy

In this talk I discuss intersecting brane configurations coming from explicit metrics with G_2 holonomy. An example of a 7-manifold which representing a R^3 bundle over a self-dual Einstein space is described and the potential appearing after compactification over the 6-d twistor space is derived.Comment: 7 pages, Latex, talk presented at the 35th Symposium Ahrenshoop, August 200

Detectable primordial non-gaussianities and gravitational waves in k-inflation

An inflationary single field model with a non-trivial kinetic term for the inflaton is discussed. It is shown that it is possible to have large primordial non-gaussianities and large tensor-to-scalar ratio in a simple concrete model with just a scalar field and a generalized kinetic term for the inflaton field. This is potentially interesting in the prospect of new forthcoming observations.Comment: 4 pages, 1 figure, REVTEX, to appear in PR

Possible link of a structurally driven spin flip transition and the insulator-metal transition in the perovskite La1−x_{1-x}Bax_{x}CoO3_{3}

The complex nature of the magnetic ground state in La$_{1-x}$A$_{x}$CoO$_{3}$ (A = Ca, Sr, Ba) has been investigated via neutron scattering. It was previously observed that ferromagnetic (FM) as well as antiferromagnetic (AFM) correlations can coexist prior to the insulator-metal transition (IMT). We focused on a unique region in the Ba phase diagram, from x = 0.17 - 0.22, in which a commensurate AFM phase appears first with a propagation vector, k = (0, -0.5, 0.5), and the Co moment in the (001)$_{R}$ plane of the rhombohedral lattice. With increasing x, the AFM component weakens while an FM order appears with the FM Co moment directed along the (001)$_{R}$ (=(111)$_{C}$) axis. By x = 0.22, a spin flip to new FM component appears as the crystal fully transforms to an orthorhombic (Pnma) structure, with the Co moments pointing along a new direction, (001)$_{O}$ (=(110)$_{C}$). It is the emergence of the magnetic Pnma phase that leads to IMT.Comment: 5 page