12,289 research outputs found
Quadratic forms and linear algebraic groups
Topics discussed at the workshop Quadratic Forms and Linear Algebraic Groups included besides the algebraic theory of quadratic and Hermitian forms and their Witt groups several aspects of the theory of linear algebraic groups and homogeneous varieties, as well as some arithmetic aspects pertaining to the theory of quadratic forms over function fields over local fields
Properties of GRB Host Galaxies
The transients following GRB970228 and GRB970508 showed that these (and
probably all) GRBs are cosmological. However, the host galaxies expected to be
associated with these and other bursts are largely absent, indicating that
either bursts are further than expected or the host galaxies are underluminous.
This apparent discrepancy does not invalidate the cosmological hypothesis, but
instead host galaxy observations can test more sophisticated models.Comment: 5 pages, AIPPROC LaTeX, to appear in "Gamma-Ray Bursts, 4th
Huntsville Symposium," eds. C. Meegan, R. Preece and T. Koshu
Local-global principles for Galois cohomology
This paper proves local-global principles for Galois cohomology groups over
function fields of curves that are defined over a complete discretely
valued field. We show in particular that such principles hold for , for all . This is motivated by work of Kato and others, where
such principles were shown in related cases for . Using our results in
combination with cohomological invariants, we obtain local-global principles
for torsors and related algebraic structures over . Our arguments rely on
ideas from patching as well as the Bloch-Kato conjecture.Comment: 32 pages. Some changes of notation. Statement of Lemma 2.4.4
corrected. Lemma 3.3.2 strengthened and made a proposition. Some proofs
modified to fix or clarify specific points or to streamline the presentatio
A comparison between obstructions to local-global principles over semiglobal fields
We consider local-global principles for rational points on varieties, in
particular torsors, over one-variable function fields over complete discretely
valued fields. There are several notions of such principles, arising either
from the valuation theory of the function field, or from the geometry of a
regular model of the function field. Our results compare the corresponding
obstructions, proving in particular that a local-global principle with respect
to valuations implies a local-global principle with respect to a sufficiently
fine regular model.Comment: 10 pages; published versio
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