Adams operations and Galois structure

We present a new method for determining the Galois module structure of the cohomology of coherent sheaves on varieties over the integers with a tame action of a finite group. This uses a novel Adams-Riemann-Roch type theorem obtained by combining the Kunneth formula with localization in equivariant K-theory and classical results about cyclotomic fields. As an application, we show two conjectures of Chinburg-Pappas-Taylor, in the case of curves.Comment: 30 pp, few additional change

On the preservation of unitarity during black hole evolution and information extraction from its interior

For more than 30 years the discovery that black holes radiate like black bodies of specific temperature has triggered a multitude of puzzling questions concerning their nature and the fate of information that goes down the black hole during its lifetime. The most tricky issue in what is known as information loss paradox is the apparent violation of unitarity during the formation/evaporation process of black holes. A new idea is proposed based on the combination of our knowledge on Hawking radiation as well as the Einstein-Podolsky-Rosen phenomenon, that could resolve the paradox and spare physicists from the unpalatable idea that unitarity can ultimately be violated even under special conditions.Comment: 8 pages, no figure

An accurate metric for the spacetime around neutron stars

The problem of having an accurate description of the spacetime around neutron stars is of great astrophysical interest. For astrophysical applications, one needs to have a metric that captures all the properties of the spacetime around a neutron star. Furthermore, an accurate appropriately parameterised metric, i.e., a metric that is given in terms of parameters that are directly related to the physical structure of the neutron star, could be used to solve the inverse problem, which is to infer the properties of the structure of a neutron star from astrophysical observations. In this work we present such an approximate stationary and axisymmetric metric for the exterior of neutron stars, which is constructed using the Ernst formalism and is parameterised by the relativistic multipole moments of the central object. This metric is given in terms of an expansion on the Weyl-Papapetrou coordinates with the multipole moments as free parameters and is shown to be extremely accurate in capturing the physical properties of a neutron star spacetime as they are calculated numerically in general relativity. Because the metric is given in terms of an expansion, the expressions are much simpler and easier to implement, in contrast to previous approaches. For the parameterisation of the metric in general relativity, the recently discovered universal 3-hair relations are used to produce a 3-parameter metric. Finally, a straightforward extension of this metric is given for scalar-tensor theories with a massless scalar field, which also admit a formulation in terms of an Ernst potential

Disclaiming Property

Can Congress pick and choose when it must follow the Constitution? One would expect not, and yet the Supreme Court has allowed it to do so. In multiple statutory programs, Congress has disclaimed constitutional property protections for valuable interests that otherwise serve as property. The result is billions of dollars’ worth of “disclaimed property” that can be bought, sold, mortgaged, or leased, but that can also be revoked at any moment without due process or just compensation. Disclaimed property already represents a great source of value, and property disclaimers are at the core of major recent policies ranging from natural resource management to intellectual property governance. As legislatures continue with market-based regulations for environmental concerns or licensing arrangements for the sharing economy, the use of disclaimed property is poised to expand even further. As a relatively recent phenomenon, property disclaimers have gone largely unconsidered by courts and scholars, but their increased importance now calls for closer study. Accordingly, this Article offers a practical and theoretical analysis of disclaimed property. It begins by examining property disclaimers arising in contexts that range from natural resources to intellectual property. It then synthesizes the judicial treatment of these interests and offers a model for valuing constitutional property protections. Building upon this background, it evaluates the constitutionality of property disclaimers as well as the policy justifications for such provisions. After a doctrinal and economic analysis, it ultimately concludes that while property disclaimers raise significant political process concerns, they may be constitutional nonetheless. However, the Article also concludes that property disclaimers are apt to be ineffective in their pursuit of legislative flexibility. Thus, this Article counsels that despite the current use and likely expansion of property disclaimers, they do not represent a beneficial or desirable policy tool

Distributed, Nega-, and Reclaimed: Setting Expectations in the New Resource Base

At this point in time, environmental law faces the task of drawing a budget for living within our resource means, and this budget will be tightly stretched. It must provide energy, water, food, and materials to a growing population; it must cope with the depletion of formerly abundant resources; and it must act both to mitigate climate impacts and adapt to the changes already manifesting. To do this, the budgeting must consider resources and uses that have previously been considered insignificant and that have not received attention in terms of ownership, allocation, or governance. Thus, the future of environmental law will involve charting individual property expectations in previously unconsidered resources: society\u27s cast-offs, scraps, and leavings. The history of environmental law has involved defining and refining expectations in property and resource use. Environmental law has addressed the resource impacts of development, set parameters for further resource development, and resolved conflicting uses or claims to resources. In each of these ways, environmental law has served to establish and adjust expectations. Thus, in a generalized sense, environmental law can be described as the governance of resource use with a particular attention to the impacts on the human and natural environment. The future of environmental law will be a variation on this past. It will still involve defining and refining expectations, only this time for a fresh set of new resources, ripe to be utilized. Well, at least for a semi-fresh set of new-ish resources, but certainly ones that are ripe to be utilized. This emerging resource stock is cobbled from formerly insignificant discards and leftovers. For example, new resource stocks can be found in wastewater streams used as water and energy sources, roofs and backyards assembled as power and food production spaces, and foregone consumption considered to be an alternative to increased supply. Distributed generation, nega-watts, reclaimed sewage, conserved water, vacant-lot farming, and rooftop gardens: these are the new resource base, and a major role for environmental law will be in figuring out how to manage them for their maximum potential benefit