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- DAVID HARBATER, Julia Hartmann, Daniel Krashen
- 2009

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 toâ€¦ (More)

We introduce a smooth projective variety T d,n which compactifies the space of configurations of n distinct points on affine d-space modulo translation and homothety. The points in the boundaryâ€¦ (More)

- Daniel Krashen
- 2005

The aim of this paper is to study the group of zero dimensional cycles in the Chow group of an algebraic variety X modulo rational equivalence. To do this we introduce geometric methods involvingâ€¦ (More)

- Daniel Krashen
- 2008

Grothendieck-Chow motives of quadric hypersurfaces have provided many insights into the theory of quadratic forms. Subsequently, the landscape of motives of more general projective homogeneousâ€¦ (More)

- Daniel Krashen
- 2002

A conjecture of Amitsur states that two Severi-Brauer varieties are birationally isomorphic if and only if the underlying algebras are the same degree and generate the same cyclic subgroup of theâ€¦ (More)

- DAVID HARBATER, Julia Hartmann, Daniel Krashen
- 2009

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 posedâ€¦ (More)

- David Harbater, Julia Hartmann, Daniel Krashen
- 2010

Local-global principles have long been an important part of number theory, beginning with the Hasse principle for quadratic forms over number fields F . This classical form of the principle, whichâ€¦ (More)

- Daniel Krashen
- 2008

We use twisted sheaves to study the problem of index reduction for Brauer classes. In general terms, this problem may be phrased as follows: given a field k, a k-variety X, and a class Î± âˆˆ Br(k),â€¦ (More)

We introduce a smooth projective variety T d,n which may be viewed either as a compactification of the space of n distinct points on affine d-space modulo translation and homothety or as aâ€¦ (More)

- Daniel Krashen
- 2007

Given a field F , an Ã©tale extension L/F and an Azumaya algebra A/L, one knows that there are extensions E/F such that AâŠ—F E is a split algebra over L âŠ—F E. In this paper we bound the degree of aâ€¦ (More)