Daniel Krashen
University of Georgia
Network
Latest external collaboration on country level. Dive into details by clicking on the dots.
Publication
Featured researches published by Daniel Krashen.
Inventiones Mathematicae | 2009
David Harbater; Julia Hartmann; Daniel Krashen
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 (in Preprint arXiv:0708.3128, 2007) on the u-invariant of p-adic function fields, p≠2. The strategy relies on a local-global principle for homogeneous spaces for rational algebraic groups, combined with local computations.
American Journal of Mathematics | 2015
David Harbater; Julia Hartmann; Daniel Krashen
We consider local-global principles for torsors under linear algebraic groups, over function fields of curves over complete discretely valued fields. The obstruction to such a principle is a version of the Tate-Shafarevich group; and for groups with rational components, we compute it explicitly and show that it is finite. This yields necessary and sufficient conditions for local-global principles to hold. Our results rely on first obtaining a Mayer-Vietoris sequence for Galois cohomology and then showing that torsors can be patched. We also give new applications to quadratic forms and central simple algebras.
Transactions of the American Mathematical Society | 2011
David Harbater; Julia Hartmann; Daniel Krashen
Given a field F, one may ask which finite groups are Galois groups of field extensions E/F such that E is a maximal subfield of a division algebra with center F. This question was originally posed by Schacher, who gave partial results over the field of rational numbers. Using patching, we give a complete characterization of such groups in the case that F is the function field of a curve over a complete discretely valued field with algebraically closed residue field of characteristic zero, as well as results in related cases.
Commentarii Mathematici Helvetici | 2014
David Harbater; Julia Hartmann; Daniel Krashen
This paper proves local-global principles for Galois cohomology groups over function fields
International Mathematics Research Notices | 2015
David Harbater; Julia Hartmann; Daniel Krashen
F
arXiv: Algebraic Geometry | 2010
Daniel Krashen
of curves that are defined over a complete discretely valued field. We show in particular that such principles hold for
Transactions of the American Mathematical Society | 2010
Daniel Krashen
H^n(F, Z/mZ(n-1))
arXiv: Rings and Algebras | 2015
Daniel Krashen; Eliyahu Matzri
, for all
Israel Journal of Mathematics | 2012
Mirela Çiperiani; Daniel Krashen
n>1
Advances in Mathematics | 2017
Benjamin Antieau; Daniel Krashen; Matthew Ward
. This is motivated by work of Kato and others, where such principles were shown in related cases for