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 $F$ of curves that are defined over a complete discretely valued field. We show in particular that such principles hold for $H^n(F, Z/mZ(n-1))$, for all $n>1$. This is motivated by work of Kato and others, where such principles were shown in related cases for $n=3$. Using our results in combination with cohomological invariants, we obtain local-global principles for torsors and related algebraic structures over $F$. 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