6,500 research outputs found
On the cycle class map for zero-cycles over local fields
We study the Chow group of zero-cycles of smooth projective varieties over
local and strictly local fields. We prove in particular the injectivity of the
cycle class map to integral l-adic cohomology for a large class of surfaces
with positive geometric genus, over local fields of residue characteristic
different from l. The same statement holds for semistable K3 surfaces defined
over C((t)), but does not hold in general for surfaces over strictly local
fields.Comment: 37 pages (with an appendix by Spencer Bloch); bibliography updated,
final versio
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
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