Graded change of ring

We investigate scalar restriction, scalar extension, and scalar coextension functors for graded modules, including their interplay with coarsening functors, graded tensor products, and graded Hom functors. This leads to several characterisations of epimorphisms of graded rings.Comment: To appear in Quaestiones Mathematica

Quasicoherent sheaves on toric schemes

Let X be the toric scheme over a ring R associated with a fan Sigma. It is shown that there are a group B, a B-graded R-algebra S and a graded ideal I of S such that there is an essentially surjective, exact functor ~ from the category of B-graded S-modules to the category of quasicoherent O_X-modules that vanishes on I-torsion modules and that induces for every B-graded S-module F a surjection Xi_F from the set of I-saturated graded sub-S-modules of F onto the set of quasicoherent sub-O_X-modules of ~F. If Sigma is simplicial, the above data can be chosen such that ~ vanishes precisely on I-torsion modules and that Xi_F is bijective for every F. In case R is noetherian, a toric version of the Serre-Grothendieck correspondence is proven, relating sheaf cohomology on X with B-graded local cohomology with support in I.Comment: To appear in Expositiones Mathematicae; corrected typo

Geographic Centroid Routing for Vehicular Networks

A number of geolocation-based Delay Tolerant Networking (DTN) routing protocols have been shown to perform well in selected simulation and mobility scenarios. However, the suitability of these mechanisms for vehicular networks utilizing widely-available inexpensive Global Positioning System (GPS) hardware has not been evaluated. We propose a novel geolocation-based routing primitive (Centroid Routing) that is resilient to the measurement errors commonly present in low-cost GPS devices. Using this notion of Centroids, we construct two novel routing protocols and evaluate their performance with respect to positional errors as well as traditional DTN routing metrics. We show that they outperform existing approaches by a significant margin.Comment: 6 page