7,802 research outputs found
The period-index problem for real surfaces
We study when the period and the index of a class in the Brauer group of the
function field of a real algebraic surface coincide. We prove that it is always
the case if the surface has no real points (more generally, if the class
vanishes in restriction to the real points of the locus where it is
well-defined), and give a necessary and sufficient condition for unramified
classes. As an application, we show that the u-invariant of the function field
of a real algebraic surface is equal to 4, answering questions of Lang and
Pfister. Our strategy relies on a new Hodge-theoretic approach to de Jong's
period-index theorem on complex surfaces.Comment: 39 pages, minor modification
Hyperconvex representations and exponential growth
Let be a real algebraic semi-simple Lie group and be the
fundamental group of a compact negatively curved manifold. In this article we
study the limit cone, introduced by Benoist, and the growth indicator function,
introduced by Quint, for a class of representations
admitting a equivariant map from to the Furstenberg boundary
of 's symmetric space together with a transversality condition. We then
study how these objects vary with the representation
Critical Fields of mesoscopic superconductors
Recent measurements have shown oscillations in the upper critical field of
simply connected mesoscopic superconductors. A quantitative theory of these
effects is given here on the basis of a Ginzburg-Landau description. For small
fields, the phase boundary exhibits a cusp where the screening currents
change sign for the first time thus defining a lower critical field .
In the limit where many flux quanta are threading the sample, nucleation occurs
at the boundary and the upper critical field becomes identical with the surface
critical field .Comment: 5 pages (Revtex and 2 PostScript figures), to apppear in Z. Phys.
- …