There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation like one obtained from the ADM equations. Unfortunately, the type of the ADM equations is not well understood and therefore we shall discuss, in the next sec...

There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation like one obtained from the ADM equations. Unfortunately, the type of the ADM equations is not well understood and therefore we shall discuss, in the next sec...

Let f : X → Spec(Z) be an arithmetic variety of dimension d ≥ 2 and (H, k) an arithmetically ample Hermitian line bundle on X, that is, a Hermitian line bundle with the following properties: (1) H is f -ample. (2) The Chern form c1(H∞, k) gives a Kähler form on X∞. (3) For every irreducible horizontal subvariety Y (i.e. Y is flat over Spec(Z)), the height ĉ1( (H, k)|Y ) dim Y of Y is positive. ...

Comodules over Hopf algebroids are of central importance in algebraic topology. It is well-known that a Hopf algebroid is the same thing as a presheaf of groupoids on Aff , the opposite category of commutative rings. We show in this paper that a comodule is the same thing as a quasi-coherent sheaf over this presheaf of groupoids. We prove the general theorem that internal equivalences of preshe...

The similarity of the observed densities of baryons and cold dark matter suggests that they have a common or related origin. This can be understood in the context of the MSSM with right-handed (RH) sneutrinos if cold dark matter is due to a d = 4 flat direction condensate of weakly coupled RH sneutrino LSPs and the baryon asymmetry is generated by Affleck-Dine leptogenesis along the d = 4 (HuL)...

In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It was proved that a pairwise weakly Lindelof property is not a hereditary property.

We analyse perturbatively, whether a flat background with vanishing G-flux in Hořava-Witten supergravity represents a vacuum state, which is stable with respect to interactions between the ten-dimensional boundaries, mediated through the D=11 supergravity bulk fields. For this, we consider fluctuations in the graviton, gravitino and 3-form around the flat background, which couple to the boundar...