13 research outputs found
Applications of patching to quadratic forms and central simple algebras
This paper provides applications of patching to quadratic forms and central
simple algebras over function fields of curves over henselian valued fields. In
particular, we use a patching approach to reprove and generalize a recent
result of Parimala and Suresh on the u-invariant of p-adic function fields, for
p odd. The strategy relies on a local-global principle for homogeneous spaces
for rational algebraic groups, combined with local computations.Comment: 48 pages; connectivity now required in the definition of rational
group; beginning of Section 4 reorganized; other minor change
Narrative inquiry into (re)imagining alternative schools: a case study of Kevin Gonzales.
Although there are many alternative schools that strive for the successful education for their students, negative images of alternative schools persist. While some alternative schools are viewed as âidealistic havens,â many are viewed as âdumping grounds,â or âjuvenile detention centers.â Employing narrative inquiry, this article interrogates how a student, Kevin Gonzales, experiences his alternative education and raises questions about the role of alternative schools. Kevin Gonzalesâs story is presented in a literary form of biographical journal to provide a âmetaphoric loftâ that helps us imagine other students like Kevin. This, in turn, provokes us to examine our current educational practice, and to (re)imagine ways in which alternative education can provide the best possible educational experiences for disenfranchised students who are increasingly underserved by the public education system